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Analytic solutions of the generalized water wave dynamical equations based on time-space symmetric differential operator

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Journal of Ocean Engineering and Science 2020年第2期5卷 186-195页

作者： Rabha W.Ibrahim Chandrashekhar Meshram Samir B.Hadid Shaher Momani Cloud Computing Center University MalayaMalaysia Department of Mathematics and Computer Science Rani Durgavati UniversityJabalpurIndia Department of Mathematics and Sciences College of Humanities and SciencesAjman UniversityAjmanUAE Department of Mathematics Faculty of ScienceUniversity of JordanAmman 11942Jordan

It is well known that there is a deep connection between the symmetric and traveling wave *** has been shown that all symmetric waves are traveling *** this paper,we establish new analytic solution collections of nonlinear conformable time-fractional water wave dynamical equation in a complex *** this purpose,we construct a new definition of a symmetric conformable differential operator(SCDO).The operator has a symmetric representation in the open unit *** using SCDO,we generalize a class of water wave dynamical equation type time-space fractional complex Ginzburg-Landau *** results show that the obtainable approaches are powerful,dependable and prepared to apply to all classes of complex differential equations.

关键词： Analytic solution Conformable calculus Fractional calculus water wave equations Majorization Subordination and superordination

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Dispersive Blow-Up Ⅱ.Schrdinger-Type equations,Optical and Oceanic Rogue waves

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Chinese Annals of Mathematics,Series B 2010年第6期31卷 793-818页

作者： Jerry L.BONA Jean-Claude SAUT Department of Mathematics Statistics and Computer Science University of Illinois at Chicago Laboratoire de Mathématiques UMR 8628 Université Paris-Sud et CNRS

Addressed here is the occurrence of point singularities which owe to the focusing of short or long waves, a phenomenon labeled dispersive blow-up. The context of this investigation is linear and nonlinear, strongly dispersive equations or systems of equations. The present essay deals with linear and nonlinear Schrdinger equations, a class of fractional order Schrdinger equations and the linearized water wave equations, with and without surface tension. Commentary about how the results may bear upon the formation of rogue waves in fluid and optical environments is also included.

关键词： Rogue waves Dispersive blow-up Nonlinear dispersive equations Nonlinear Schrdinger equation water wave equations Propagation in optical cables Weak turbulence models

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On Local Singularities in Ideal Potential Flows with Free Surface

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Chinese Annals of Mathematics,Series B 2019年第6期40卷 925-948页

作者： Jian-Guo LIU Robert L.PEGO Department of Physics and Department of Mathematics Duke UniversityDurhamNC 27708USA Department of Mathematical Sciences and Center for Nonlinear Analysis Carnegie Mellon UniversityPittsburghPennsylvaniaPA 12513USA

Despite important advances in the mathematical analysis of the Euler equations for water waves,especially over the last two decades,it is not yet known whether local singularities can develop from smooth data in well-posed initial value *** ideal free-surface flow with zero surface tension and gravity,the authors review existing works that describe"splash singularities",singular hyperbolic solutions related to jet formation and"flip-through",and a recent construction of a singular free surface by Zubarev and Karabut that however involves unbounded negative *** authors illustrate some of these phenomena with numerical computations of 2D flow based upon a conformal mapping *** tests with a different kind of initial data suggest the possibility that corner singularities may form in an unstable way from specially prepared initial data.

关键词： Incompressible flow water wave equations Splash singularity Flipthrough Dirichlet hyperbolas Conformal mapping

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