We study solitary waves in the cylindrical Kadomtsev-Petviashvili equation designated to media with positive dispersion (the cKP1 equation). By means of Darboux-Matveev transform, we derive exact solutions that describe two-dimensional (lumps), lump chains, and their interactions. One obtained describes modulation instability outgoing ring solitons disintegration onto a number lumps. also describing decaying lumps chains complex spatial structure-ripplons. Then, normal anomalous (resonant)...

We revise soliton and lump solutions described by the cylindrical Kadomtsev–Petviashvili (cKP) equation construct new exact relevant to physical observation. In first part of this study, we consider basically axisymmetric waves Kortweg–de Vries analyze approximate equation. Then, stability solitons with respect azimuthal perturbations suggest a criterion instability. The results our numerical modeling confirm suggested reveal emergence in course development modulation instability ring...

Soliton molecules were first discovered in optical systems and are currently a hot topic of research. We obtain soliton the (2+1)-dimensional fifth-order KdV system under new resonance condition called velocity theory. On basis molecules, asymmetric solitons can be obtained by selecting appropriate parameters. Based on N-soliton solution, we hybrid solutions consisting lump waves breather partial long wave limits. some types special solutions, stable meaning that interactions among elastic....

Based on the hybrid solutions to (2+1)-dimensional Kadomtsev–Petviashvili (KP) equation, motion trajectory of KP equation is further studied. We obtain a single lump before and after collision with line, lump, breather waves by approximating along some parallel orbits at infinity. derive mathematical expression phase change wave. At same time, we give plots reveal obvious change. Our method proposed find wave can be applied other integrable equations. The results expand understanding...

Based on velocity resonance and Darboux transformation, soliton molecules hybrid solutions consisting of smooth positons are derived. Two new interesting results obtained: the first is that relationship between clearly pointed out, second we find two different interactions called strong interaction weak interaction, respectively. The will only disappear when t → ∞. This can also excite some periodic phenomena.

Abstract Using the Hirota bilinear method, we derive resonant solutions to KP1 equation. Solutions describe lump chains differently oriented in ( x , y )-plane. We show that arise as limiting case of more general non-resonant when phase shifts caused by their interaction become infinite. Resonant can both stationary patterns (for example, Y-shaped consisting three different chains) and non-stationary interacting parallel chains. In latter case, a chain be emitted/absorbed another chain. As...

Abstract In this paper, a new general bilinear Bäcklund transformation and Lax pair for the (2+1)-dimensional shallow water wave equation are given in terms of binary Bell polynomials. Based on along with introducing an arbitrary function, multi-kink soliton, line breather, multi-line rogue solutions non-flat constant background plane derived. Further, we found that dynamic pattern breather periodic waves similar to two-periodic obtained through multi-dimensional Riemann theta function....

Abstract In this paper, a series of ripple waves with decay modes for the ‐dimensions Kadomtsev–Petviashvili equation, always viewed as nonintegrable KP are investigated. The mode wave solutions including ripplon, lump ripples, and chain ripples described by Airy function, all constructed from Gram determinant form. Their propagation dynamics behavior is studied, comprehensive analysis asymptotic properties these has been diligently conducted.