Localized wave solutions of a higher-order short pulse equation
College of Mathematics and Systems Science, Shandong University of Science and Technology, 266590, Qingdao, Shandong, People’s Republic of China
Accepted: 14 February 2023
Published online: 8 March 2023
Constructing suitable Lax pair and making use of zero-curvature equation, a higher-order short pulse equation is researched and proved to be Lax integrable. Modulational instability of the above equation is investigated, which is an important possible generation mechanism of localized wave solutions. Then higher-order semi-rational soliton, multi-soliton and breather solutions of the higher-order short pulse equation are derived by generalized Darboux transformation and classical Darboux transformation of a new Lax pair obtained by hodograph transformation, which are represented by the ratio of the corresponding two determinants. Dynamics of these localized wave solutions are represented in several figures and certain important physical quantities for one-loop soliton solutions are analyzed, such as amplitude, wave number, wave width, velocity and initial phase. In particular, Darboux matrices under classical Darboux transformation of negative expansion, positive expansion and positive and negative expansion are given.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.