On weak compactons to the nonlinearly dispersive mK(m, n, a, b) equation

Jingqun Wang; Jian-Gen Liu; Chunyan Qin; Jingqun Wang; Jian-Gen Liu; Chunyan Qin

doi:10.3934/math.2026943

AIMS Mathematics

2026, Volume 11, Issue 7: 23393-23403. doi: 10.3934/math.2026943

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On weak compactons to the nonlinearly dispersive mK(m, n, a, b) equation

1.
School of Mathematics and Statistics, Suzhou University of Technology, Changshu 215500, Jiangsu, China
2.
School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, Jiangsu, China
3.
School of Mathematics and Statistics, Suzhou University, Suzhou 234000, Anhui, China

Received: 23 May 2026 Revised: 14 July 2026 Accepted: 17 July 2026 Published: 31 July 2026
MSC : 35C07, 37K10, 37K40

In this paper, we investigated the precise existence conditions for weak compacton solutions of the nonlinearly dispersive mK(m, n, a, b) equation. By employing cutoff conditions, we derived a complete classification of parameters for compacton solutions. Specifically, Theorem 3.1 established four sets of sufficient conditions (Rt1–Rt4) under which a traveling wave solution possessed compact support. For the special parameters $ a = b-1 $, $ m = 1 $, and $ n = 2b $, we derived the corresponding traveling wave ordinary differential equation and present explicit conserved integrals for mass, momentum, and energy. Furthermore, in Theorem 4.1, we provided general quadrature formulae for the compacton solutions. The results extend other studies on the mK(m, n, a, b) systems and offer an analytical framework for compacton existence in nonlinear dispersive equations.
- mK(m, n, a, b) equation,
- solitary waves,
- weak compactons
Citation: Jingqun Wang, Jian-Gen Liu, Chunyan Qin. On weak compactons to the nonlinearly dispersive mK(m, n, a, b) equation[J]. AIMS Mathematics, 2026, 11(7): 23393-23403. doi: 10.3934/math.2026943

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Abstract

In this paper, we investigated the precise existence conditions for weak compacton solutions of the nonlinearly dispersive mK(m, n, a, b) equation. By employing cutoff conditions, we derived a complete classification of parameters for compacton solutions. Specifically, Theorem 3.1 established four sets of sufficient conditions (Rt1–Rt4) under which a traveling wave solution possessed compact support. For the special parameters $ a = b-1 $, $ m = 1 $, and $ n = 2b $, we derived the corresponding traveling wave ordinary differential equation and present explicit conserved integrals for mass, momentum, and energy. Furthermore, in Theorem 4.1, we provided general quadrature formulae for the compacton solutions. The results extend other studies on the mK(m, n, a, b) systems and offer an analytical framework for compacton existence in nonlinear dispersive equations.

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