Characteristics of solitary wave, homoclinic breather wave and rogue wave solutions in a (2+1)-dimensional generalized breaking soliton equation

Solitary Wave and Quasi-Periodic Wave Solutions to a (3+1)-Dimensional Generalized Calogero-Bogoyavlenskii-Schiff Equation

“…It is also integrable by the one-dimensional inverse scattering transform and Painléve test [28][29][30][31]. Recently, more and more people are interested in studying some generalized nonlinear evolution equations [32][33][34][35][36][37][38], resulting from their more widely applications in many physical fields [39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54]. To our knowledge, Riemann theta function periodic wave solutions for Eq.…”

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

“…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. More importantly, collision will happen among different solitons.…”

A New Nonlinear Equation with Lump‐Soliton, Lump‐Periodic, and Lump‐Periodic‐Soliton Solutions

“…Many high-dimensional NPDEs admit the lump solutions such as the Ishimori-I equation [19], the Kadomtsev-Petviashvili (KP) equation [20], the generalized KP equation [21], the variable-coefficient nonlinear Schrödinger equation [22], the KP-Boussinesq equation [23], and the Sawada-Kotera equation [24]. In order to describe complex situations, some interaction solutions are constructed by the localization procedure related with the nonlocal symmetry [25][26][27] and the homoclinic breather limit approach [28,29]. By mixing a positive quadratic function with the exponential/trigonometric functions, interactive lump-kink [30][31][32][33][34][35], lump-soliton [36][37][38], and lumpperiodic waves [39] of the NPDEs have been presented.…”