Journal ArticleDOI
Painlevé analysis and invariant solutions of generalized fifth-order nonlinear integrable equation
Lakhveer Kaur,Abdul-Majid Wazwaz +1 more
TLDR
In this article, a generalized fifth-order nonlinear integrable equation has been investigated by locating movable critical points with aid of Painleve analysis and it has been found that this equation passes painleve test for $$\alpha =\beta $$ which implies affirmation toward the complete integrability.Abstract:
In present work, new form of generalized fifth-order nonlinear integrable equation has been investigated by locating movable critical points with aid of Painleve analysis and it has been found that this equation passes Painleve test for $$\alpha =\beta $$
which implies affirmation toward the complete integrability. Lie symmetry analysis is implemented to obtain the infinitesimals of the group of transformations of underlying equation, which has been further pre-owned to furnish reduced ordinary differential equations. These are then used to establish new abundant exact group-invariant solutions involving various arbitrary constants in a uniform manner.read more
Citations
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Lie symmetry analysis, optimal system and conservation laws of a new (2+1)-dimensional KdV system
TL;DR: In this paper, Lie point symmetries of a new (2+1)-dimensional KdV system are constructed by using the symbolic computation software Maple, and the one-dimensional optimal system associated with corresponding Lie algebra is obtained.
Journal ArticleDOI
Painlevé analysis for a new (3 +1 )-dimensional KP equation: Multiple-soliton and lump solutions
TL;DR: In this article , the authors proposed a new (3 + 1)-dimensional Kadomtsev-Petviashvili (KP) equation and verified the integrability of this equation using the Painlevé analysis.
Journal ArticleDOI
Novel technique to investigate the convergence analysis of the tempered fractional natural transform method applied to diffusion equations
TL;DR: In this article , the authors used a new technique called the Tempered Fractional Natural Transform Method (TFNTM) to find exact solutions to tempered fractional convection-diffusion equations and the Black-Scholes equation.
Journal ArticleDOI
Exact closed-form solutions and dynamics of solitons for a $$(2+1)$$-dimensional universal hierarchy equation via Lie approach
Sachin Kumar,Monika Niwas +1 more
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Nonlinear control for soliton interactions in optical fiber systems
TL;DR: In this article, the authors considered the fifth-order nonlinear Schrodinger equation with variable dispersion and nonlinear effects to realize soliton control and improve soliton quality.
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
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
Exact Solution of the Korteweg-de Vries Equation for Multiple Collisions of Solitons
TL;DR: An exact solution for the Korteweg-de Vries equation for the case of multiple collisions of $N$ solitons with different amplitudes was obtained in this paper, which is the only known exact solution.