Compact and noncompact structures formed by nonlinear equations with positive and negative exponents

摘要

This paper presents a study on compact and noncompact structures formed by nonlinear dispersive equations with positive and negative exponents. The work examines two genuinely nonlinear equations. The focusing branch exhibits compactons: solitons with the absence of infinite wings, whereas the defocusing branch supports solutions with solitary patterns. The work formally shows that equation with positive exponent and equation with negative exponent each leads to a different physical structure.