Lump-type Soliton Research Articles

Emergence and Interaction of the Lump-Type Solution with the (3+1)-D Jimbo-Miwa Equation

Abstract A kinky breather-soliton solution and kinky periodic-soliton solution are obtained using Hirota’s bilinear method and homoclinic test approach for the (3+1)-dimensional Jimbo-Miwa equation. Based on these two exact solutions, some lump-type solutions are emerged by limit behaviour. Meanwhile, two kinds of new dynamical phenomena, kinky breather degeneracy and kinky periodic degeneracy, are discussed and presented. Finally, the interaction between a stripe soliton and a lump-type soliton is discussed by the standardisation of the lump-type solution; the fusion and fission phenomena of soliton solutions are investigated and simulated by three-dimensional plots.

Soliton and Riemann theta function quasi-periodic wave solutions for a $$(2+1)$$ ( 2 + 1 ) -dimensional generalized shallow water wave equation

In this paper, a $$(2 + 1)$$ -dimensional generalized shallow water wave equation is investigated through bilinear Hirota method. Interestingly, the breather-type and lump-type soliton solutions are obtained. Furthermore, dynamic properties of the soliton waves are revealed by means of the asymptotic analysis. Based on Hirota bilinear method and Riemann theta function, we succeed in constructing quasi-periodic wave solutions with a generalized form. We also display the asymptotic properties of these quasi-periodic wave solutions and point out the relation between the quasi-periodic wave solutions and the soliton solutions.

The Generation Of Lump Solitons By A Bottom Topography In A Surface-Tension Dominated Flow

The generation of lump solitons by a three-dimensional bottom topography is numerically investigated by use of a forced Kadomtsev-Petviashvili-I (KP-I) equation. The numerical method is based on the third order Runge-Kutta method and the Crank-Nicolson scheme. The main result is the pairwise periodic generation of two pairs of lump-type solitons downstream of the obstacle. The pair with the smaller amplitude is generated with a longer period and moves in a larger angle with respect to the positive x-axis than the one with the larger amplitude. Furthermore, the effects of the detuning parameter on the generation and evolution of lumps are studied. Finally the waves propagating upstream of the obstacle are also briefly investigated.