Extended F-Expansion Method for Solving the modified Korteweg-de Vries (mKdV) Equation

Abstract

One of the phenomenon in marine science that is often encountered is the phenomenon of water waves. Waves that occur below the surface of seawater are called internal waves. One of the mathematical models that can represent solitary internal waves is the modified Korteweg-de Vries (mKdV) equation. Many methods can be used to construct the solution of the mKdV wave equation, one of which is the extended F-expansion method. The purpose of this study is to determine the solution of the mKdV wave equation using the extended F-expansion method. The result of solving the mKdV wave equation is the exact solutions. The exact solutions of the mKdV wave equation are expressed in the Jacobi elliptic functions, trigonometric functions, and hyperbolic functions. From this research, it is expected to be able to add insight and knowledge about the implementation of the innovative methods for solving wave equations.

Non‐singular complexiton, singular complexiton and complex multiple soliton solutions to the (3 + 1)‐dimensional nonlinear evolution equation

“…Soliton theory is an important part of nonlinear scientific content, and finding efficacious approaches to develop soliton solutions is the hot spot for scholars. As yet, a good many reliable and efficacious techniques have been put forward to solve the NPDEs, for example, the Bäcklund transformation approach [13–15], direct algebraic approach [16], Darboux transformation technique [17–19], subequation approach [20–22], trial‐equation technique [23–25], extended F‐Expansion approach [26, 27], exp‐function approach [28, 29], and many others [30–36]. In the presented study, we will inquire into the (3 + 1)‐dimensional nonlinear evolution equation (NEE) that reads as [37]: where the inverse operator is defined as: …”

Multi-lump, resonant Y-shape soliton, complex multi kink solitons and the solitary wave solutions to the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation for incompressible fluid

“…As is well known, a series of important principles such as the linear superposition principle of solutions no longer hold for NPDEs, so there is no universal method for solving the NPDEs. Although there is no universal and effective method for obtaining the exact solutions to NPDEs, several approaches for constructing the exact solutions for the NPDEs have been put forward in different applicable situations such as the extended F-expansion technique [1][2][3][4], Darboux transformation approach [5][6][7], general integral technique [8], unified Riccati equation approach [9], Bäcklund transformation [10][11][12][13], exp-function method [14][15][16][17], Subequation technique [18][19][20], tanh function method [21,22], (G′/G)-expansion approach [23,24] and many others [25][26][27][28][29]. In this exploration, we aim to give a study to the (2+1)-dimensional BLMPE, which reads as:…”

Characteristics of dynamic waves in incompressible fluid regarding nonlinear Boiti-Leon-Manna-Pempinelli model

“…In this context, several computational approaches have been developed by researchers. Instantly, Backlund transformation [5], first integral method [6], Jacobi elliptic function scheme [7,8], extended simplest equation technique [9][10][11], F-expansion method [12,13], trial equation scheme [14,15], various rational ( ) / G G ¢ -expansion tools [16][17][18], exp-function approach [19,20], improved tanh approach [21], Darboux transformation approach [22], different Hirota schemes [23][24][25][26][27], Kudryashov technique [28] etc. This present study is conducted by implementing two competent techniques such as improved tanh and improved auxiliary equation.…”