Journal ArticleDOI
Dynamics of soliton waves of group-invariant solutions through optimal system of an extended KP-like equation in higher dimensions of medical sciences and mathematical physics
TLDR
In this paper , the robust technique of the Lie group theory of differential equation was invoked to achieve analytic solutions to the equation, which is used in a systematic way to generate the Lie point symmetries of the equation under study.About:
This article is published in Journal of Geometry and Physics.The article was published on 2022-04-01. It has received 10 citations till now. The article focuses on the topics: Soliton & Partial differential equation.read more
Citations
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Variational and non-variational approaches with Lie algebra of a generalized (3 + 1)-dimensional nonlinear potential Yu-Toda-Sasa-Fukuyama equation in Engineering and Physics
TL;DR: In this article , the authors presented the analytical investigation of a completely generalized (3 + 1)-dimensional nonlinear potential Yu-Toda-Sasa-Fukuyama equation which has applications in the fields of engineering and physics.
Journal ArticleDOI
Bifurcation Theory, Lie Group-Invariant Solutions of Subalgebras and Conservation Laws of a Generalized (2 + 1)-Dimensional BK Equation Type II in Plasma Physics and Fluid Mechanics
TL;DR: In this paper , a (2+1)-dimensional generalized Bogoyavlensky-Konopelchenko equation was studied and the authors obtained a five-dimensional Lie algebra of the equation through Lie group analysis.
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First integrals, solutions and conservation laws of the derivative nonlinear Schrödinger equation
TL;DR: In this article , the derivative nonlinear Schrödinger equation has been studied for the propagation of circular polarized nonlinear Alfvén waves in plasmas using first integrals.
Journal ArticleDOI
Optimal solutions of Lie subalgebra, dynamical system, travelling wave solutions and conserved currents of (3+1)-dimensional generalized Zakharov–Kuznetsov equation type I
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Lie group theory, stability analysis with dispersion property, new soliton solutions and conserved quantities of 3D generalized nonlinear wave equation in liquid containing gas bubbles with applications in mechanics of fluids, biomedical sciences and cell biology
TL;DR: In this paper , a generalized nonlinear wave equation in a fluid accommodating gas fizzes with applications is presented. But, the analytical investigations accomplished on a three dimensional generalized nonsmooth wave equation with applications in biomedical sciences, biomedical sciences and biological cells are discussed.
References
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Book
Applications of Lie Groups to Differential Equations
TL;DR: In this paper, the Cauchy-Kovalevskaya Theorem has been used to define a set of invariant solutions for differential functions in a Lie Group.
Book
Darboux transformations and solitons
V. B. Matveev,Mikhail A. Salle +1 more
TL;DR: In this paper, the authors developed a systematic algebraic approach to solve linear and non-linear partial differential equations arising in soliton theory, such as the non-stationary linear Schrodinger equation, Korteweg-de Vries and Kadomtsev-Petviashvili equations, the Davey Stewartson system, Sine-Gordon and nonlinearSchrodinger equations 1+1 and 2+1 Toda lattice equations, and many others.
Journal ArticleDOI
Exp-function method for nonlinear wave equations
Ji-Huan He,Xu-Hong Wu +1 more
TL;DR: In this article, a new method, called Exp-function method, is proposed to seek solitary solutions, periodic solutions and compacton-like solutions of nonlinear differential equations, and the modified KdV equation and Dodd-Bullough-Mikhailov equation are chosen to illustrate the effectiveness and convenience of the suggested method.
Journal ArticleDOI
Simplest equation method to look for exact solutions of nonlinear differential equations
TL;DR: In this paper, a new method is presented to look for exact solutions of nonlinear differential equations by using the general solutions of the simplest nonlinear equations and taking into consideration all possible singularities of equation studied.
Journal ArticleDOI
On the evolution of packets of water waves
Mark J. Ablowitz,Harvey Segur +1 more
TL;DR: In this paper, the authors consider the evolution of water waves that travel predominantly in one direction, but in which the wave amplitudes are modulated slowly in both horizontal directions, and they find that the two-dimensional evolution of the wave packets depends fundamentally on the dimensionless surface tension and fluid depth.
Related Papers (5)
New symmetries, group-invariant solutions, linear differential constraints of a generalized Burgers-KdV equation and its reduction
Huanhuan Lu,Yufeng Zhang +1 more