Lump Solutions and Resonance Stripe Solitons to the (2+1)-Dimensional Sawada-Kotera Equation

Abstract

Based on the symbolic computation, a class of lump solutions to the (2+1)-dimensional Sawada-Kotera (2DSK) equation is obtained through making use of its Hirota bilinear form and one positive quadratic function. These solutions contain six parameters, four of which satisfy two determinant conditions to guarantee the analyticity and rational localization of the solutions, while the others are free. Then by adding an exponential function into the original positive quadratic function, the interaction solutions between lump solutions and one stripe soliton are derived. Furthermore, by extending this method to a general combination of positive quadratic function and hyperbolic function, the interaction solutions between lump solutions and a pair of resonance stripe solitons are provided. Some figures are given to demonstrate the dynamical properties of the lump solutions, interaction solutions between lump solutions, and stripe solitons by choosing some special parameters.

High-Order Breather Solutions, Lump Solutions, and Hybrid Solutions of a Reduced Generalized (3 + 1)-Dimensional Shallow Water Wave Equation

“…Below, we focus on the asymptotic behaviors of the periodic solutions generated by equation (23). From the quadratic dispersion relation in equation (20).…”

“…e rogue wave first appeared in studies of oceanography [13,14] and gradually spread to other fields of physics such as Bose-Einstein condensates [15,16], optical system [17], superfluid, and plasma. Recently, Ma et al proposed the positive quadratic function to obtain the lump solutions, and some special examples of lump solutions have been found, such as the KdV equation [18,19], the KP equation [20,21], the BKP equation [22], the SK equation [23], the JM equation [24], the shallow water wave equation [25], the coupled Boussinesq equations [26], and nonlinear evolution equation [27,28]. More recently, high-order rogue waves in a variety of soliton equations have been studied, including the generalized Kadomtsev-Petviashvili equation [29], nonlinear Schrödinger equation [30][31][32][33], the Boussinesq equation [34], the breaking soliton equation [35], the Sasa-Satsuma equation [36], the Davey-Stewartson equations [37], the complex short pulse equation [38], and many other equations.…”

Soliton Molecules and Some Novel Types of Hybrid Solutions to (2 + 1)-Dimensional Variable-Coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada Equation

“…Among these rational solutions, lump solutions, breather wave solutions, and rogue wave solutions are hot point all the time. Recently, the hybrid solutions of lump solutions with other types of solutions draw a lot of attention, which include lump-soliton [17][18][19], lump-kink solution [20], resonance stripe solitons [21][22][23], and some hybrid solutions [24][25][26]. Very recently, Lou [27] introduced a new possible mechanism, the velocity resonant, to form soliton molecules and asymmetric solitons of three (1 + 1)-dimensional fluid models: fifth-order KdV, SK equation, and KK equation.…”

Multi-soliton, breathers, lumps and interaction solution to the (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov equation

“…The explicit solutions of NLEEs play a prominent role in the study of nonlinear science. Various effective procedure have been developed to solve NLEEs, like the inverse scattering transform [1], the Darboux transformation [2], Backlund transformation [3], the unified method (UM) and its generalized form (GUM) [4, 5] and Hirota bilinear form method [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]. The Hirota's bilinear method is one of the most direct and convenient method to obtain the exact soliton solution of NLEEs.…”