New exact wave solutions of the variable-coefficient (1 + 1)-dimensional Benjamin-Bona-Mahony and (2 + 1)-dimensional asymmetric Nizhnik-Novikov-Veselov equations via the generalized exponential rational function method
@article{Ghanbari2019NewEW, title={New exact wave solutions of the variable-coefficient (1 + 1)-dimensional Benjamin-Bona-Mahony and (2 + 1)-dimensional asymmetric Nizhnik-Novikov-Veselov equations via the generalized exponential rational function method}, author={Behzad Ghanbari and Chun-Ku Kuo}, journal={The European Physical Journal Plus}, year={2019}, volume={134}, pages={1-13}, url={https://api.semanticscholar.org/CorpusID:197402061} }
Abstract.In this paper, the variable-coefficient (1 + 1)-dimensional Benjamin-Bona-Mahony (BBM) and (2 + 1)-dimensional asymmetric Nizhnik-Novikov-Veselov (ANNV) equations are investigated via the generalized exponential rational function method (GERFM). This paper proceeds step-by-step with increasing detail about derivation processes, first illustrating the algorithms of the proposed method and then exploiting an even deeper connection between the derived solutions with the GERFM. As a result…
79 Citations
New exact solutions of (3+1)-dimensional modified KdV-Zakharov-Kuznetsov equation by Sardar-subequation method
- 2023
Mathematics, Physics
New solitary wave solutions are developed for various shapes of three-dimensional nonlinear partial differential equations using the Sardar-Subequation method. Some periodic solitary wave solutions,…
The applications of symbolic computation to exact wave solutions of two HSI-like equations in (2+1)-dimensional
- 2023
Mathematics, Physics
It is renowned that Hirota–Satsuma–Ito (HSI) equation is widely used to study wave dynamics of shallow water. In this work, two new HSI-like equations are investigated which could be extended to…
On determining some exact wave solutions to the Nizhnik–Novikov–Veselov system via a rebuts technique
- 2021
Physics, Mathematics
Dynamics of Lump, Breather, Two-Waves and Other Interaction Solutions of (2+1)-Dimensional KdV Equation
- 2023
Physics
In this investigation, we address a particular variant of the Korteweg–de Vries (KdV) equation, specifically focusing on the (2+1)-dimensional KdV equation. The equation can model various physical…
Abundant wave solutions to two novel KP-like equations using an effective integration method
- 2021
Physics, Mathematics
In this work, two new nonlinear evolution equations arising from the B-type Kadomtsev-Petviashvili equation, called BKP-like equations, are investigated. The integration technique that used in this…
Applications of two kinds of Kudryashov methods for time fractional (2 + 1) dimensional Chaffee–Infante equation and its stability analysis
- 2024
Mathematics, Physics
In this study, the beta time fractional (2 + 1) dimensional Chaffee–Infante equation used to describe the behavior of gas diffusion in a homogeneous medium is discussed. Generalized Kudryashov and…
Analysis of soliton solutions with different wave configurations to the fractional coupled nonlinear Schrödinger equations and applications
- 2023
Physics, Mathematics
In this research, we address the problem of solving (1 + 1)-dimensional fractional coupled nonlinear Schrödinger equations (FCNLSE) with beta derivatives, which are essential for understanding wave…
On the Solitary Wave Solutions to the (2+1)-Dimensional Davey-Stewartson Equations
- 2019
Mathematics
In this article, by using the Bernoulli sub-equation, we build the analytical traveling wave solution of the (2+1)-dimensional Davey-Stewartson equation system. First of all, the imaginary…
Abundant optical solitons to the (2+1)-dimensional Kundu-Mukherjee-Naskar equation in fiber communication systems
- 2023
Physics, Engineering
The Kundu-Mukherjee-Naskar equation holds significant relevance as a nonlinear model for investigating intricate wave phenomena in fluid and optical systems. This study uncovers new optical soliton…
21 References
Resonant multi-soliton solutions to new (3+1)-dimensional Jimbo–Miwa equations by applying the linear superposition principle
- 2019
Physics
In this paper, the linear superposition principle and Hirota bilinear equations are simultaneously employed to handle two new (3+1)-dimensional Jimbo–Miwa equations. The corresponding resonant…
The modified (G/G)-expansion method for the (1+1) Hirota-Ramani and (2+1) breaking soliton equation
- 2013
Physics
In this article, we apply the modified (G'/G)-expansion method to construct hyperbolic, trigonometric and rational function solutions of nonlinear evolution equations. This method can be thought of…
On breather waves, rogue waves and solitary waves to a generalized (2+1)-dimensional Camassa-Holm-Kadomtsev-Petviashvili equation
- 2018
Physics, Mathematics
A new generalized exponential rational function method to find exact special solutions for the resonance nonlinear Schrödinger equation
- 2018
Physics
Abstract.The present paper suggests a novel technique to acquire exact solutions of nonlinear partial differential equations. The main idea of the method is to generalize the exponential rational…
Solitary and Jacobi elliptic wave solutions of the generalized Benjamin-Bona-Mahony equation
- 2017
Mathematics
Whitham–Broer–Kaup–Like equations and coupled Hirota–Satsuma KdV equations
- 2009
Mathematics, Physics
The extended G^'G-expansion method is proposed to seek exact solutions of nonlinear evolution equations to construct travelling wave solutions of Whitham-Broer-Kaup-Like equations and coupled Hirota-Satsuma KdV equations.
Lump soliton, mixed lump stripe and periodic lump solutions of a (2 + 1)-dimensional asymmetrical Nizhnik–Novikov–Veselov equation
- 2017
Physics, Mathematics
The lump soliton solutions of a (2 + 1)-dimensional asymmetrical Nizhnik–Novikov–Veselov equation are obtained by making use of its bilinear form. We discuss the conditions to guarantee the…