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A Novel Approach with Time-splitting spectral Technique for the Coupled schrdinger–Boussinesq Equations Involving Riesz Fractional Derivative

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Communications in Theoretical Physics 2017年第9期67卷 301-308页

作者： s.saha ray Department of Mathematics National Institute Technology

In the present paper the Riesz fractional coupled schr6dinger-Boussinesq （s-B） equations have been solved by the time-splitting Fourier spectral （TsFs） method. This proposed technique is utilized for discretizing the schrodinger like equation and further, a pseudospectral discretization has been employed for the Boussinesq-like equation. Apart from that an implicit finite difference approach has also been proposed to compare the results with the solutions obtained from the time-splitting technique. Furthermore, the time-splitting method is proved to be unconditionally stable. The error norms along with the graphical solutions have also been presented here.

关键词： coupled schrsdinger-Boussinesq equations Riesz fractional derivative discrete fourier transform inverse discrete Fourier transform

New Exact solutions for the Wick-Type stochastic Kudryashov–sinelshchikov Equation

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Communications in Theoretical Physics 2017年第2期67卷 197-206页

作者： s.saha ray s.singh Department of Mathematics National Institute Technology Rourkela Orissa-769008 India

In this article, exact solutions of Wick-type stochastic Kudryashov–sinelshchikov equation have been obtained by using improved sub-equation method. We have used Hermite transform for transforming the Wick-type stochastic Kudryashov–sinelshchikov equation to deterministic partial differential equation. Also we have applied inverse Hermite transform for obtaining a set of stochastic solutions in the white noise space.

关键词： Kudryashov–sinelshchikov Wick-product White noise space improved sub-equation method Hermite transform inverse Hermite transform

Higher-order approximate solutions of fractional stochastic point kinetics equations in nuclear reactor dynamics

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Nuclear science and Techniques 2019年第3期30卷 114-126页

作者： s.singh s.saha ray Department of Mathematics National Institute of Technology Rourkela

stochastic point kinetics equations(sPKEs) are a system of Ito? stochastic differential equations whose solution has been obtained by higher-order *** this study, a fractional model of sPKEs has been analyzed. The efficiency of the proposed higher-order approximation scheme has been discussed in the results section. The solutions of sPKEs in the presence of Newtonian temperature feedback have also been provided to further discuss the physical behavior of the fractional model.

关键词： Fractional stochastic point reactor kinetics equations Fractional calculus Higher-order approximation Caputo derivative Neutron population

New Exact solutions of Fractional Zakharov–Kuznetsov and Modified Zakharov–Kuznetsov Equations Using Fractional sub-Equation Method

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Communications in Theoretical Physics 2015年第1期63卷 25-30页

作者： s.saha ray s.sahoo Department of Mathematics National Institute of Technology Rourkela Orissa- 769008 India

In the present paper, we construct the analytical exact solutions of some nonlinear evolution equations in mathematical physics; namely the space-time fractional Zakharov–Kuznetsov(ZK) and modified Zakharov–Kuznetsov(m ZK) equations by using fractional sub-equation method. As a result, new types of exact analytical solutions are obtained. The obtained results are shown graphically. Here the fractional derivative is described in the Jumarie's modified Riemann–Liouville sense.

关键词： fractional sub-equation method space-time fractional Zakharov-Kuznetsov (ZK) equation space-time fractional modified Zakharov-Kuznetsov (mZK) equation modified Riemann-Liouvillederivative Mittag-leffler function

Painlevé analysis,auto-Bäcklund transformation and new exact solutions of(2+1)and(3+1)-dimensional extended sakovich equation with time dependent variable coefficients in ocean physics

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Journal of Ocean Engineering and science 2023年第3期8卷 246-262页

作者： shailendra singh s.saha ray National Institute of Technology Department of MathematicsRourkela 769008India

This article considers time-dependent variable coefficients(2+1)and(3+1)-dimensional extended sakovich ***éanalysis and auto-Bäcklund transformation methods are used to examine both the considered ***éanalysis is appeared to test the integrability while an auto-Bäcklund transformation method is being presented to derive new analytic soliton solution families for both the considered *** new family of exact analytical solutions are being obtained success-fully for each of the considered *** soliton solutions in the form of rational and exponential functions are being *** results are also expressed graphically to illustrate the potential and physical behaviour of both *** the considered equations have applications in ocean wave theory as they depict new solitary wave soliton solutions by 3D and 2D graphs.

关键词： (2+1)-dimensional extended sakovich equation (3+1)-dimensional extended sakovich equation Auto-Bäcklund transformation Painlevéanalysis solitary wave solution

Two efficient reliable methods for solving fractional fifth order modified sawada-Kotera equation appearing in mathematical physics

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Journal of Ocean Engineering and science 2016年第3期1卷 219-225页

作者： s.saha ray s.sahoo National Institute of Technology Department of MathematicsRourkela 769008India

The present paper deals with two reliable efficient methods ***-sech method and modified Kudryashov method,which are used to solve time-fractional nonlinear evolution *** delineating the legitimacy of proposed methods,we employ it to the time-fractional fifth-order modified sawada-Kotera *** a consequence,we effectively obtained more new exact solutions for time-fractional fifth-order modified sawada-Kotera *** have also presented the numerical simulations for time-fractional fifth-order modified sawada-Kotera equation by means of three dimensional plots.

关键词： Time-fractional fifth-order modified sawada-Kotera equation Local fractional calculus Tanh-sech method Modified Kudryashov method

Numerical solutions of stochastic Fisher equation to study migration and population behavior in biological invasion

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International Journal of Biomathematics 2017年第7期10卷 205-218页

作者： s. singh s. saha ray Department of Mathematics National Institute of Technology Rourkela Rourkela 769008 India

In this paper, numerical solutions of the stochastic Fisher equation have been obtained by using a semi-implicit finite difference scheme. The samples for the Wiener process have been obtained from cylindrical Wiener process and Q-Wiener process. stability and convergence of the proposed finite difference scheme have been discussed scrupulously. The sample paths obtained from cylindrical Wiener process and Q-Wiener process have also been shown graphically.

关键词： stochastic Fisher equation Q-Wiener process Euler-Maruyama scheme L2(D)-valued Q-Wiener process circular embedding cylindrical Wiener process.

New exact solutions of coupled Boussinesq-Burgers equations by Exp-function method

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Journal of Ocean Engineering and science 2017年第1期2卷 34-46页

作者： L.K.Ravi s.saha ray s.sahoo National Institute of Technology Department of MathematicsRourkela 769008India

In the present paper,we build the new analytical exact solutions of a nonlinear differential equation,specifically,coupled Boussinesq-Burgers equations by means of Exp-function ***,we analyze the results by plotting the three dimensional soliton graphs for each case,which exhibit the simplicity and effectiveness of the proposed *** primary purpose of this paper is to employ a new approach,which allows us victorious and efficient derivation of the new analytical exact solutions for the coupled Boussinesq-Burgers equations.

关键词： Exp-function method solitary wave solutions Non-linear evolution equations Coupled Boussinesq-Burgers equations

New Optical soliton solutions of Nolinear Evolution Equation Describing Nonlinear Dispersion

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Communications in Theoretical Physics 2019年第9期71卷 1063-1068页

作者： saud Owyed M.A.Abdou Abdel-Haleem Abdel-Aty s.saha ray Department of Mathematics College of SciencesUniversity of BishaBisha61922P.O.Box344Saudi Arabia Department of Physics College of SciencesUniversity of BishaBisha61922P.O.Box344Saudi Arabia Physics Department Faculty of SciencesAl-Azhar University71524AssiutEgypt Department of Mathematics National Institute of TechnologyRourkela769008OdishaIndia

In this work, we examine two algorithm schemes, namely, Kudryashov expansion and Auxiliary equation method for obtaining new optical soliton solutions of the discrete electrical lattice models in nonlinear scheme(salerno equation). Our solutions obtained here are include the hyperbolic, rational, and trigonometric functions. Our two used methods are proved to be effective and powerful methods in obtaining the exact solutions of nonlinear evolution equations(NLEEs).

关键词： discrete electrical lattice generalized Kudryashov expansion method auxiliary equation method exact solutions