Abstract
In this paper, we employ mapping methods to construct exact travelling wave solutions for a modified Korteweg-de Vries equation. We have derived periodic wave solutions in terms of Jacobi elliptic functions, kink solutions and singular wave solutions in terms of hyperbolic functions.
Highlights
Travelling wave solutions (TWSs) of nonlinear evolution equations have been extensively studied due to their significant applications in mathematical theory and other fields in physical sciences
The advantage of using travelling wave solutions is that the governing partial differential equation (PDE) reduces to an ordinary differential equation (ODE) which makes it easier to solve
Several methods using TWSs have been proposed such as the tanh method [1], the exponential function method [2], the Jacobi elliptic function (JEF) method [3], mapping methods [47] etc
Summary
Travelling wave solutions (TWSs) of nonlinear evolution equations have been extensively studied due to their significant applications in mathematical theory and other fields in physical sciences. Solitary wave solutions (SWSs) of different types of Korteweg-de Vries (KdV) equations have been a field of intense study in many branches of Physics over several decades [8,9,10,11]. We derive periodic wave solutions (PWSs) of a modified KdV equation in terms of JEFs [12] and deduce their infinite period counterparts in terms of hyperbolic functions such as shock wave solutions and singular wave solutions using mapping methods. The mapping methods employed in this paper give a variety of solutions, such as hyperbolic function solutions, different types of JEFs etc., which other methods cannot do
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