Multisoliton solutions of the (2+1)-dimensional Harry Dym equation

Resonant multi-soliton solutions to the (2 + 1)-dimensional Sawada–Kotera equations via the simplified form of the linear superposition principle

“…In summary, the sign of k i determines the wave fusion/fission. Our results are similar to the dynamics reported for the (2+1)-dimensional Harry Dym equation in [20] and the mKP-II equation in [16]. However, to the author's best knowledge, the propagation of inelastic interactions to the (2+1)-dimensional SK equation have not been reported in the previous literature.…”

“…There have two scenarios to the inelastic soliton interactions called soliton resonances: a single solitary wave splits into several solitary waves, or multiple solitary waves fuse into a single solitary wave. This phenomenon can be demonstrated by multi-soliton solutions without phase shifts, namely resonant multisoliton solutions, and has been observed and discussed in the (2+1)-dimensional Harry Dym equation, mKP-II equation, and others [16][17][18][19][20][21][22][23]. In other words, the resonant waves play key roles in the inelastic interaction mechanism and are worthy of further study.…”

Dressing chain for the acoustic spectral problem

“…The construction of the extended chains of Darboux and Laplace transformations for 2 + 1-dimensional equations with variable separant seems to be straightforward. As a typical example one can take the generalized Dym equation studied in the papers [28,29].…”

Bounded Traveling Wave Solutions and Their Relations for the Generalized HD Type Equation

“…Different kinds of solutions to the HD equation have been derived by some authors [17][18][19]. Moreover, the (2 + 1)dimensional HD equation [20,21], coupled HD hierarchy [22,23], and generalized HD equation [24,25] were studied. In 2015, Geng et al [26] first propose a hierarchy of a generalized HD type (gHD type) equation:…”