Exact Traveling Wave Solutions of the Loaded Modified Korteweg-de Vries Equation

Abstract

This paper is dedicated to finding the traveling wave solutions of the loaded modified Korteweg-de Vries equation. It is shown to find the solutions via (G’/G) — expansion method which is one of the most effective ways of finding solutions. When the parameters are taken as special values the solitary waves are also derived from the traveling waves. The traveling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. This method is easy to implement using well-known software packages, which allows you to solve complex nonlinear evolution equations of mathematical physics.

Integration of the Loaded Negative Order Korteweg-De Vries Equation in the Class of Periodic Functions

“…Based on these data, we find q(0, t). After, substitute the found expression for q(0, t) into equation (15), and solving the Cauchy problem for an arbitrary value τ , we find ξ n (τ, t), n ≥ 1. By the trace formula (16) we determine q(x, t) and then from the formula (17) we determine p 2 (x, t).…”

“…The (G /G) -expansion method was used to integrate the loaded Kortewegde Vries (KdV) equation and the loaded modified Korteweg-de Vries (mKdV) equation in [14,15,16].…”

Generalized (G'/G) - Expansion Method and its Applications to the Loaded Burgers Equation

“…Integration of the loaded modified Korteweg-de Vries (mKdV) equation in the class of periodic functions was treated in [18]. (G ′ /G) -expansion method was used for the integrations of loaded Korteweg-de Vries (KdV) equation and the loaded modified Korteweg-de Vries (mKdV) equation in [19,20].…”

The linear Fredholm integral equations with functionals and parameters

“…Loaded equations appear in many applications, see e.g. [11,12]. But theory and numerical methods for the loaded integral equations remained less developed.…”