What question did this study set out to answer?

The aim is to find solitary and shock wave solutions for the perturbed Kawahara equation.

February 23, 2026Examples and Counterexamples0 citationsOpen Access

Solitary waves and shock waves for the perturbed Kawahara equation

LKLakhveer KaurJaypee Institute of Information Technology AAAhmed H. ArnousKhazar University ICIbrahim Zeghaiton Chaloob

Key Points

The aim is to find solitary and shock wave solutions for the perturbed Kawahara equation.
Utilized the generalized G ′ / G –expansion methodology.
Focused on retrieving singular solitary wave and shock wave solutions.
Analyzed parameter constraints for solution existence.
Identified specific conditions for the existence of solitary waves.
Recovered several shock wave solutions that are mathematically significant.

Abstract

This paper retrieves singular soliyary waves and shock wave solutions to the perturbed Kawahara equation that describes shallow water wave dynamics. The generalized G ′ / G –expansion methodology is implemented to recover these solutions. The solitary waves appear with parameter constraints that are enlisted for the existence of such solutions.

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