<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

Published Online: Jun 15, 2023

Page range: 2209 - 2228

Received: Aug 23, 2022

Accepted: Dec 19, 2022

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

Keywords
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

Published Online: Jun 15, 2023

Page range: 2209 - 2228

Received: Aug 23, 2022

Accepted: Dec 19, 2022

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

Keywordsnew 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.

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