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Solitons and other solutions to Wu–Zhang system
(Vilnius University, 2017)
This paper addresses Wu–Zhang system to study dispersive long waves. The extended
trial equation method extracts solitary waves, shock waves, and singular solitary waves solutions.
Subsequently, Lie group formalism is ...
Time fractional Biswas–Milovic equation: Group analysis, soliton solutions, conservation laws and residual power series solution
(Elsevier, 2019)
In this work, we studied time fractional Biswas–Milovic equation (FBME) which describes the long distance optical communication with Kerr law nonlinearity. We analyzed group analysis of equation by using Lie symmetry ...
Invariant traveling wave solutions of parity-time-symmetric mixed linear-nonlinear optical lattices with three types of nonlinearity
(Institute of Physics Publishing, 2019)
This paper focuses on the complex nonlinear Schrö dinger equation for the propagation of optical pulses in the nonlinear media with imprinted parity-time symmetric mixed linear-nonlinear optical lattices. Three types of ...
Symmetry analysis of some nonlinear generalised systems of space–time fractional partial differential equations with time-dependent variable coefficients
(Springer, 2019)
In this paper, the Lie group analysis method is applied to carry out the Lie point symmetries of some space–time fractional systems including coupled Burgers equations, Ito’s system, coupled Korteweg–de-Vries (KdV) equations, ...
Time fractional Biswas–Milovic equation: Group analysis, soliton solutions, conservation laws and residual power series solution
(Elsevier GmbH, 2019)
In this work, we studied time fractional Biswas–Milovic equation (FBME) which describes the long distance optical communication with Kerr law nonlinearity. We analyzed group analysis of equation by using Lie symmetry ...
Soliton Solutions of�Dual-mode Kawahara Equation via�Lie Symmetry Analysis
(Springer Science and Business Media Deutschland GmbH, 2022-06-29)
In this article, we investigate a newly proposed dual-mode Kawahara equation. Our main aim in this paper is to find out the soliton and periodic solutions of the Kawahara equation. Initially, we reduce the governing equation ...
Highly dispersive W�shaped and other optical solitons with quadratic�cubic nonlinearity: Symmetry analysis and new Kudryashov's method
(Elsevier Ltd, 2023-06-24)
Lie symmetry analysis is utilized in this paper to explore the properties of highly dispersive optical solitons that exhibit quadratic�cubic self-phase modulation. The use of Lie symmetry analysis enables the reduction of ...
The integrable Boussinesq equation and it�s breather, lump and soliton solutions
(Springer Science and Business Media B.V., 2022-01-17)
The fourth-order nonlinear Boussinesq water wave equation, which explains the propagation of long waves in shallow water, is explored in this article. We used the Lie symmetry approach to analyze the Lie symmetries and ...
A generalized (2+1)-dimensional Hirota bilinear equation: integrability, solitons and invariant solutions
(Springer Science and Business Media B.V., 2022-11-11)
In this paper, we consider an extended form of generalized (2 + 1) -dimensional Hirota bilinear equation which demonstrates nonlinear wave phenomena in shallow water, oceanography and nonlinear optics. We have successfully ...
A (2+1)-dimensional Kadomtsev�Petviashvili equation with competing dispersion effect: Painlev� analysis, dynamical behavior and invariant solutions
(Elsevier B.V., 2021-03-09)
In this paper, we concern ourselves with the nonlinear Kadomtsev�Petviashvili equation (KP) with a competing dispersion effect. First we examine the integrability of governing equation via using the Painlev� analysis. We ...