Physics

Korteweg–de Vries equation

Nonlinear system

Symmetry (geometry)

Mathematics

Mathematical physics

Biology

Infinitesimal

Partial differential equation

Elliptic function

Symbolic computation

Mathematical analysis

Ecology

Geometry

Type (biology)

Maple

Botany

Quantum mechanics

Differential equation

Applied mathematics

Ordinary differential equation

Results in Physics

In this article, we aim to employ two analytical methods including, the Lie symmetry method and the Jacobi elliptical solutions finder method to acquire exact solitary wave solutions in various forms of (1+1)-dimensional Kawahara–KdV type equation and modified Kawahara–KdV type equation. These models are famous models that arise in the modeling of many complex physical phenomena. At the outset, we have generated geometric vector fields and infinitesimal generators of Kawahara–KdV type equations. The (1+1)-dimensional Kawahara–KdV type equations reduced into ordinary differential equations (ODEs) using Lie symmetry reductions. Furthermore, numerous exact solitary wave solutions are obtained utilizing the Jacobi elliptical solutions finder method with the help of symbolic computation with Maple. The obtained results are new in the formulation, and more useful to explain complex physical phenomena. The results reveal that these mathematical approaches are straightforward, effective, and powerful methods that can be adopted for solving other nonlinear evolution equations.

The Lie symmetry analysis and exact Jacobi elliptic solutions for the Kawahara–KdV type equations