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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A new (3+1)-dimensional Kadomtsev–Petviashvili equation and its integrability, multiple-solitons, breathers and lump waves
TL;DR: A new (3+1)-dimensional integrable Kadomtsev–Petviashvili equation is developed and its integrability is verified by the Painleve analysis, and the abundant dynamical behaviors for these solutions are discovered.
Journal ArticleDOI
Complex simplified Hirota’s forms and Lie symmetry analysis for multiple real and complex soliton solutions of the modified KdV–Sine-Gordon equation
Abdul-Majid Wazwaz,Lakhveer Kaur +1 more
TL;DR: In this paper, a detailed exploration of modified KdV-Sine-Gordon equation in integrable form, owning to two-component nonlinear channel for modeling laser light propagation, is presented.
Journal ArticleDOI
Optical solitons for nonlinear Schrödinger (NLS) equation in normal dispersive regimes
Abdul-Majid Wazwaz,Lakhveer Kaur +1 more
TL;DR: In this article, a variational iteration method for obtaining exact analytical solutions for nonlinear Schrodinger (NLSE) equation with normal dispersive regimes was proposed, where a set of diverse types of optical dark solitons were furnished with significant physical perspective.
Journal ArticleDOI
Nonlinear waves behaviors for a coupled generalized nonlinear Schrödinger–Boussinesq system in a homogeneous magnetized plasma
Zhong-Zhou Lan,Bo-Ling Guo +1 more
TL;DR: In this paper, a coupled generalized nonlinear Schrodinger-Boussinesq system was investigated, where the upper-hybrid and magneto-acoustic modes in a homogeneous magnetized plasma for the bidirectional propagation near the magnetoacoustic speed.
Journal ArticleDOI
Optical bright and dark soliton solutions for coupled nonlinear Schrödinger (CNLS) equations by the variational iteration method
TL;DR: In this article, a variational iteration method was used to derive a set of diverse types of bright and dark optical soliton solutions for coupled nonlinear Schrodinger (CNLS) equations in the anomalous and dispersive regimes.
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.