Journal ArticleDOI
Dynamical Soliton Wave Structures of One-Dimensional Lie Subalgebras via Group-Invariant Solutions of a Higher-Dimensional Soliton Equation with Various Applications in Ocean Physics and Mechatronics Engineering
About:
This article is published in Communications on Applied Mathematics and Computation.The article was published on 2022-07-20. It has received 6 citations till now. The article focuses on the topics: Lie group & Invariant (physics).read more
Citations
More filters
Journal ArticleDOI
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.
Journal ArticleDOI
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.
Journal ArticleDOI
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
References
More filters
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
Solitons, Nonlinear Evolution Equations and Inverse Scattering
M. A. Ablowitz,Peter A. Clarkson +1 more
TL;DR: In this article, the authors bring together several aspects of soliton theory currently only available in research papers, including inverse scattering in multi-dimensions, integrable nonlinear evolution equations in multidimensional space, and the ∂ method.
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.
Related Papers (5)
Invariant tori for a nonlinearly modified Kawahara equation with periodic boundary conditions
Vibration of plates using plate characteristic functions obtained by reduction of partial differential equation
Rama B. Bhat,G. Mundkur +1 more