Lump waves and their dynamics in a generalized Kadomtsev–Petviashvili-like model
Wen‐Xiu Ma
Abstract
This study explores dispersion-induced lump structures in a generalized (2+1)-dimensional Kadomtsev–Petviashvili-like framework. Starting from a generalized bilinear representation of the governing equation, we derive positive quadratic wave solutions through symbolic computation, which yield lump structures. The analysis reveals that the stationary points of these quadratic waves lie along a straight line in the spatial domain and move at constant velocities. Along this characteristic line, the lump wave amplitude becomes zero. The development of these lump waves is attributed to the combined effects of five distinct dispersion terms in the model.
Topics & Concepts
PhysicsQuadratic equationBilinear interpolationClassical mechanicsAmplitudeRepresentation (politics)Constant (computer programming)Mathematical analysisDispersion (optics)Dynamics (music)Dispersion relationBilinear formDomain (mathematical analysis)Rogue waveLine (geometry)Mathematical physicsQuadratic functionWave propagationNonlinear systemMixing (physics)Point (geometry)Real lineConnection (principal bundle)Longitudinal waveNonlinear Waves and SolitonsNonlinear Photonic SystemsFractional Differential Equations Solutions