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Abundant closed-form wave solutions and dynamical structures of soliton solutions to the (3+1)-dimensional BLMP equation in mathematical physics

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Journal of Ocean Engineering and Science 2022年第2期7卷 178-187页

作者： Sachin kumar Amit kumar Department of Mathematics Faculty of Mathematical SciencesUniversity of DelhiDelhi 110007India Department of Mathematics Sri Vankateswara CollegeUniversity of DelhiDelhi 110021India

The physical principles of natural occurrences are frequently examined using nonlinear evolution equa-tions(NLEEs).Nonlinear equations are intensively investigated in mathematical physics,ocean physics,scientific applications,and marine engineering.This paper investigates the Boiti-Leon-Manna-Pempinelli(BLMP)equation in(3+1)-dimensions,which describes fluid propagation and can be considered as a non-linear complex physical model for incompressible fluids in plasma physics.This four-dimensional BLMP equation is certainly a dynamical nonlinear evolution equation in real-world applications.Here,we im-plement the generalized exponential rational function(GERF)method and the generalized Kudryashov method to obtain the exact closed-form solutions of the considered BLMP equation and construct novel solitary wave solutions,including hyperbolic and trigonometric functions,and exponential rational func-tions with arbitrary constant parameters.These two efficient methods are applied to extracting solitary wave solutions,dark-bright solitons,singular solitons,combo singular solitons,periodic wave solutions,singular bell-shaped solitons,kink-shaped solitons,and rational form solutions.Some three-dimensional graphics of obtained exact analytic solutions are presented by considering the suitable choice of involved free parameters.Eventually,the established results verify the capability,efficiency,and trustworthiness of the implemented methods.The techniques are effective,authentic,and straightforward mathematical tools for obtaining closed-form solutions to nonlinear partial differential equations(NLPDEs)arising in nonlinear sciences,plasma physics,and fluid dynamics.

关键词： Closed-form solutions Generalized exponential rational function method Solitons Generalized Kudryashov method Solitary waves

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Invariance analysis for determining the closed-form solutions, optimal system, and various wave profiles for a (2+1)-dimensional weakly coupled B-Type Kadomtsev-Petviashvili equations

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Journal of Ocean Engineering and Science 2023年第2期8卷 133-144页

作者： Setu Rani Sachin kumar Raj kumar Department of Mathematics Faculty of Mathematical SciencesUniversity of DelhiDelhi 110007India Department of Mathematics Kirori Mal CollegeUniversity of DelhiDelhi 110007India

In the case of negligible viscosity and surface tension,the B-KP equation shows the evolution of quasione-dimensional shallow-water waves,and it is growingly used in ocean physics,marine engineering,plasma physics,optical fibers,surface and internal oceanic waves,Bose-Einstein condensation,ferromagnetics,and string theory.Due to their importance and applications,many features and characteristics have been investigated.In this work,we attempt to perform Lie symmetry reductions and closed-form solutions to the weakly coupled B-Type Kadomtsev-Petviashvili equation using the Lie classical method.First,an optimal system based on one-dimensional subalgebras is constructed,and then all possible geometric vector yields are achieved.We can reduce system order by employing the one-dimensional optimal system.Furthermore,similarity reductions and exact solutions of the reduced equations,which include arbitrary independent functional parameters,have been derived.These newly established solutions can enhance our understanding of different nonlinear wave phenomena and dynamics.Several threedimensional and two-dimensional graphical representations are used to determine the visual impact of the produced solutions with determined parameters to demonstrate their dynamical wave profiles for various examples of Lie symmetries.Various new solitary waves,kink waves,multiple solitons,stripe soliton,and singular waveforms,as well as their propagation,have been demonstrated for the weakly coupled B-Type Kadomtsev-Petviashvili equation.Lie classical method is thus a powerful,robust,and fundamental scientific tool for dealing with NPDEs.Computational simulations are also used to prove the effectiveness of the proposed approach.

关键词： Group-invariant solutions Solitary wave solutions Lie group theory Dynamical wave structures

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Study of exact analytical solutions and various wave profiles of a new extended(2+1)-dimensional Boussinesq equation using symmetry analysis

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Journal of Ocean Engineering and Science 2022年第5期7卷 475-484页

作者： Sachin kumar Setu Rani Department of Mathematics Faculty of Mathematical SciencesUniversity of DelhiDelhi110007India

This paper systematically investigates the exact solutions to an extended(2+1)-dimensional Boussinesq equation,which arises in several physical applications,including the propagation of shallow-water waves,with the help of the Lie symmetry analysis method.We acquired the vector fields,commutation relations,optimal systems,two stages of reductions,and exact solutions to the given equation by taking advantage of the Lie group method.The method plays a crucial role to reduce the number of independent variables by one in each stage and finally forms an ODE which is solved by taking relevant suppositions and choosing the arbitrary constants that appear therein.Furthermore,Lie symmetry analysis(LSA)is implemented for perceiving the symmetries of the Boussinesq equation and then culminating the solitary wave solutions.The behavior of the obtained results for multiple cases of symmetries is obtained in the present framework and demonstrated through three-and two-dimensional dynamical wave profiles.These solutions show single soliton,multiple solitons,elastic behavior of combo soliton profiles,and stationary waves,as can be seen from the graphics.The outcomes of the present investigation manifest that the considered scheme is systematic and significant to solve nonlinear evolution equations.

关键词： Boussinesq equation Lie group method Exact invariant solutions Solitons Optimal system

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Abundant analytical soliton solutions and different wave profiles to the Kudryashov-Sinelshchikov equation in mathematical physics

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Journal of Ocean Engineering and Science 2022年第6期7卷 565-577页

作者： Sachin kumar Monika Niwas Shubham kumar Dhiman Department of Mathematics Faculty of Mathematical SciencesUniversity of DelhiDelhi 110007India

The generalized exponential rational function(GERF)method is used in this work to obtain analytic wave solutions to the Kudryashov-Sinelshchikov(K S)equation.The K S equation depicts the occurrence of pressure waves in mixtures of liquid-gas bubbles while accounting for thermal expansion and viscosity.By applying the GERF method to the KS equation,we obtain analytic solutions in terms of trigonometric,hyperbolic,and exponential functions,among others.These solutions include solitary wave solutions,dark-bright soliton solutions,singular soliton solutions,singular bell-shaped solutions,traveling wave solutions,rational form solutions,and periodic wave solutions.We discuss the two-dimensional and three-dimensional graphics of some obtained solutions under the accurate range space by selecting appropriate values for the involved arbitrary parameters to make this research more praiseworthy.The obtained analytic wave solutions specify the GERF method’s dependability,capability,trustworthiness,and efficiency.

关键词： Solitary wave solutions Closed form solutions GERF technique Dynamical wave structures

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Symmetry analysis,closed-form invariant solutions and dynamical wave structures of the generalized (3+1)-dimensional breaking soliton equation using optimal system of Lie subalgebra

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Journal of Ocean Engineering and Science 2022年第2期7卷 188-201页

作者： Monika Niwas Sachin kumar Harsha Kharbanda Department of Mathematics Faculty of Mathematical SciencesUniversity of DelhiDelhi110007India

Nonlinear evolution equations(NLEEs)are primarily relevant to nonlinear complex physical systems in a wide range of fields,including ocean physics,plasma physics,chemical physics,optical fibers,fluid dy-namics,biology physics,solid-state physics,and marine engineering.This paper investigates the Lie sym-metry analysis of a generalized(3+1)-dimensional breaking soliton equation depending on five nonzero real parameters.We derive the Lie infinitesimal generators,one-dimensional optimal system,and geo-metric vector fields via the Lie symmetry technique.First,using the three stages of symmetry reductions,we converted the generalized breaking soliton(GBS)equation into various nonlinear ordinary differential equations(NLODEs),which have the advantage of yielding a large number of exact closed-form solu-tions.All established closed-form wave solutions include special functional parameter solutions,as well as hyperbolic trigonometric function solutions,trigonometric function solutions,dark-bright solitons,bell-shaped profiles,periodic oscillating wave profiles,combo solitons,singular solitons,wave-wave interac-tion profiles,and various dynamical wave structures,which we present for the first time in this research.Eventually,the dynamical analysis of some established solutions is revealed through three-dimensional sketches via numerical simulations.Some of the new solutions are often useful and helpful for study-ing the nonlinear wave propagation and wave-wave interactions of shallow water waves in many new high-dimensional nonlinear evolution equations.

关键词： Lie symmetry technique Infinitesimal generators Optimal systems Closed-form wave solutions Solitary waves

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Evolutionary dynamics of solitary wave profiles and abundant analytical solutions to a(3+1)-dimensional burgers system in ocean physics and hydrodynamics

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Journal of Ocean Engineering and Science 2023年第1期8卷 1-14页

作者： Sachin kumar Amit kumar Brij Mohan Department of Mathematics Faculty of Mathematical SciencesUniversity of DelhiDelhi 110007India Department of Mathematics Sri Vankateswara CollegeUniversity of DelhiDelhi 110021India Department of Mathematics Hansraj CollegeUniversity of DelhiDelhi 110007India

In the fields of oceanography,hydrodynamics,and marine engineering,many mathematicians and physi-cists are interested in Burgers-type equations to show the different dynamics of nonlinear wave phenom-ena,one of which is a(3+1)-dimensional Burgers system that is currently being studied.In this paper,we apply two different analytical methods,namely the generalized Kudryashov(GK)method,and the generalized exponential rational function method,to derive abundant novel analytic exact solitary wave solutions,including multi-wave solitons,multi-wave peakon solitons,kink-wave profiles,stripe solitons,wave-wave interaction profiles,and periodic oscillating wave profiles for a(3+1)-dimensional Burgers sys-tem with the assistance of symbolic computation.By employing the generalized Kudryashov method,we obtain some new families of exact solitary wave solutions for the Burgers system.Further,we applied the generalized exponential rational function method to obtain a large number of soliton solutions in the forms of trigonometric and hyperbolic function solutions,exponential rational function solutions,peri-odic breather-wave soliton solutions,dark and bright solitons,singular periodic oscillating wave soliton solutions,and complex multi-wave solutions under various family cases.Based on soft computing via Wolfram Mathematica,all the newly established solutions are verified by back substituting them into the considered Burgers system.Eventually,the dynamical behaviors of some established results are exhibited graphically through three-and two-dimensional wave profiles via numerical simulation.

关键词： Dynamical structures Burger system GERF Method Generalized kudryashov method Closed-form solutions Solitary waves

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Specific wave profiles and closed-form soliton solutions for generalized nonlinear wave equation in(3+1)-dimensions with gas bubbles in hydrodynamics and fluids

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Journal of Ocean Engineering and Science 2023年第1期8卷 91-102页

作者： Sachin kumar Ihsanullah Hamid M.A.Abdou Department of Mathematics Faculty of Mathematical SciencesUniversity of DelhiDelhi 110007India Department of Mathematics College of SciencesUniversity of BishaP.O.Box 344Bisha 61922Saudi Arabia Physics Department Faculty of ScienceMansoura UniversityMansoura 35516Egypt

Nonlinear evolution equations(NLEEs)are frequently employed to determine the fundamental principles of natural phenomena.Nonlinear equations are studied extensively in nonlinear sciences,ocean physics,fluid dynamics,plasma physics,scientific applications,and marine engineering.The generalized exponen-tial rational function(GERF)technique is used in this article to seek several closed-form wave solutions and the evolving dynamics of different wave profiles to the generalized nonlinear wave equation in(3+1)dimensions,which explains several more nonlinear phenomena in liquids,including gas bubbles.A large number of closed-form wave solutions are generated,including trigonometric function solutions,hyper-bolic trigonometric function solutions,and exponential rational functional solutions.In the dynamics of distinct solitary waves,a variety of soliton solutions are obtained,including single soliton,multi-wave structure soliton,kink-type soliton,combo singular soliton,and singularity-form wave profiles.These de-termined solutions have never previously been published.The dynamical wave structures of some analyt-ical solutions are graphically demonstrated using three-dimensional graphics by providing suitable values to free parameters.This technique can also be used to obtain the soliton solutions of other well-known equations in engineering physics,fluid dynamics,and other fields of nonlinear sciences.

关键词： Closed-form solutions Dynamical wave patterns Analytic solutions Nonlinear wave equation GERF Method Solitary waves Solitons

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Construction of multiple new analytical soliton solutions and various dynamical behaviors to the nonlinear convection-diffusion-reaction equation with power-law nonlinearity and density-dependent diffusion via Lie symmetry approach together with a couple of integration approaches

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Journal of Ocean Engineering and Science 2023年第3期8卷 226-237页

作者： Shoukry El-Ganaini Sachin kumar Monika Niwas Department of Mathematics Faculty of ScienceDamanhour UniversityDamanhour 22514Egypt Department of Mathematics Faculty of Mathematical SciencesUniversity of DelhiDelhi 110007India Department of Mathematics University of DelhiDelhi 110007India

By taking advantage of three different computational analytical methods:the Lie symmetry analysis,the generalized Riccati equation mapping approach,and the modified Kudryashov approach,we construct multiple new analytical soliton solutions to the nonlinear convection-diffusion-reaction equation(NCDR)with power-law nonlinearity and density-dependent diffusion.Lie symmetry analysis is one of the pow-erful techniques that reduce the higher-order partial differential equation into an ordinary differential equation by reduction of independent variables.By the Lie group technique,we obtain one-parameter in-variant transformations,determining equations and corresponding vectors for the considered convection-diffusion-reaction equation.By treating the parameters of the governing equation as constants,the ap-plied methods yield a variety of new closed-form solutions,including inverse function solutions,periodic solutions,exponential function solutions,dark solitons,singular solitons,combo bright-singular solitons,and the combine of bright-dark solitons and dark-bright solitons.Moreover,using the Bäcklund transfor-mation of the generalized Riccati equation and modified Kudryashov method,we can construct multiple solitons and other solutions of the considered equation.The obtained new solutions of this work demon-strate that the used approaches are powerful and effective in dealing with nonlinear equations,and that these solutions are required to explain many biological and physical phenomena.Comparing our obtained solutions of this paper with the ones obtained in the literature,we see that our solutions are new and not reported elsewhere.These newly formed soliton solutions will be more beneficial in the various dis-ciplines of ocean engineering,plasma physics,and nonlinear sciences.

关键词： Lie symmetry analysis Generalized riccati equation mapping Modified kudryashov approach Nonlinear convection-diffusion-reaction equation Solitary wave solutions Closed form solutions Backlund transformation Exact solution Dynamical wave structures Bäcklund transformation

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Chaos detection in SIR model with modified Beddington–De Angelis type incidence rate and saturated treatment

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International Journal of Modeling, Simulation, and Scientific Computing 2021年第6期12卷 56-74页

作者： Shikha Jain Sachin kumar Department of Mathematics University of Delhi Delhi 110007India

In this paper, we construct an SIR epidemic model with a modified Beddington–DeAngelis type incidence rate and saturated treatment rate. We modify the incidence rateto incorporate the isolation of infected individuals after detection, and separation of somesusceptible individuals from the rest to avoid the infection, without an increase in thenumber of classes. We find that the system has a unique disease-free equilibrium (DFE)which is locally asymptotically stable when the reproduction number is less than unity.The multiple endemic equilibria may exist irrespective of the basic reproduction number.The existence of bistability is encountered. Supercritical transcritical (forward), as wellas subcritical transcritical (backward) bifurcation, may occur at R0 = 1 where contactrate, β = β∗ acts as the bifurcation parameter. Therefore, DFE need not be globallystable. The conditions for the existence of Andronov–Hopf bifurcation are deduced withmaximum treatment capacity, c = c0 as the bifurcation parameter. The impacts of isolation of confirmed infected cases and separation of some susceptible from rest are studiednumerically as well as the effect of saturation in treatment. The existence of chaoticbehavior is deduced by showing the maximum Lyapunov exponent to be positive as wellas the sensitivity to initial conditions. The computation of the Kalpan–Yorke dimensionto be fractional confirms the existence of fractal-type strange attractor. The positiveKolmogorov–Sinai entropy further strengthens the claim of the existence of chaos.

关键词： Beddington–De Angelis type incidence rate saturated treatment stability bifurcation Lyapunov exponent chaos

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Rate-dependent mechanical behavior of jointed rock with an impersistent joint under different infill conditions

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Journal of Rock Mechanics and Geotechnical Engineering 2022年第5期14卷 1380-1393页

作者： Sachin kumar Gaurav Tiwari Venkitanarayanan Parameswaran Arghya Das Department of Civil Engineering Indian Institute of TechnologyKanpurIndia

Transition in the rate-dependent mechanical response of rock was investigated due to the presence of impersistent joint with different infill conditions.Four types of samples,i.***.intact,jointed with no grouting,jointed and grouted with cement,and jointed and grouted with epoxy,were fabricated using model material.A series of dynamic split Hopkinson pressure bar(SHPB) tests was conducted on prepared samples with strain rates varying between 53-130 salong with static uniaxial compression tests(10s).Progression of fracture/failure along samples was monitored using high-speed imaging and digital image correlation(DIC).Strength was observed to be significantly lower for jointed samples as compared to intact samples.However,the increasing trend of strength with strain rates remained similar for all types of samples.Epoxy was observed to be a better grout due to greater improvement in the strength of epoxy grouted jointed samples than cement grouted samples under both static and dynamic conditions.Significant changes were observed in fracture behavior(initiation,pattern and mechanism)with strain rate for intact and jointed unfilled/grouted samples.Fracturing was dominated by shear and tensile cracks at high strain rates compared to tensile cracks at low strain rates in all samples.Unlike static loading conditions,the location of cracks initiation shifts away from joint tips with increasing strain rate and depending upon existing infill conditions(unfilled/grouted).

关键词： Jointed rocks Grouted joint Dynamic loading Strain rates

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