<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In the paper, a new expansion auxiliary equation method is proposed. By this method, traveling wave solutions of the simplified MCH equation and the ZKBBM equation are constructed successfully, including soliton solutions, singular solutions, triangular periodic solutions, Jacobi and Weierstrass doubly periodic solutions and other new solutions, their characteristics are demonstrated by three-dimension and two-dimension profile figures and comparisons with previous references are made. It is shown that our proposed method can obtain new and more general solutions of nonlinear evolution equations and would be a powerful mathematical tool for solving nonlinear evolution equations.</p>
</abstract>

In the paper, a new expansion auxiliary equation method is proposed. By this method, traveling wave solutions of the simplified MCH equation and the ZKBBM equation are constructed successfully, including soliton solutions, singular solutions, triangular periodic solutions, Jacobi and Weierstrass doubly periodic solutions and other new solutions, their characteristics are demonstrated by three-dimension and two-dimension profile figures and comparisons with previous references are made. It is shown that our proposed method can obtain new and more general solutions of nonlinear evolution equations and would be a powerful mathematical tool for solving nonlinear evolution equations.

A new expansion auxiliary equation method for traveling wave solutions of the simplified MCH equation and the ZKBBM equation

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

In the paper, a new expansion auxiliary equation method is proposed. By this method, traveling wave solutions of the simplified MCH equation and the ZKBBM...

A new expansion auxiliary equation method for traveling wave solutions of the simplified MCH equation and the ZKBBM equation

Publicado en línea: 15 jun 2023

Páginas: 2209 - 2228

Recibido: 23 ago 2022

Aceptado: 19 dic 2022

DOI: https://doi.org/10.2478/amns.2023.1.00406

Palabras clave
new expansion auxiliary equation method, simplified MCH equation, ZKBBM equation, soliton wave solutions, doubly periodic solutions

© 2023 Juanjuan Ji et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

A new expansion auxiliary equation method for traveling wave solutions of the simplified MCH equation and the ZKBBM equation

Publicado en línea: 15 jun 2023

Páginas: 2209 - 2228

Recibido: 23 ago 2022

Aceptado: 19 dic 2022

DOI: https://doi.org/10.2478/amns.2023.1.00406

Palabras clavenew expansion auxiliary equation method, simplified MCH equation, ZKBBM equation, soliton wave solutions, doubly periodic solutions

© 2023 Juanjuan Ji et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Palabras clave
new expansion auxiliary equation method, simplified MCH equation, ZKBBM equation, soliton wave solutions, doubly periodic solutions