Soliton molecules(SMs)of the(2+1)-dimensional generalized KonopelchenkoDubrovsky-Kaup-Kupershmidt(gKDKK)equation are found by utilizing a velocity resonance ansatz to N-soliton solutions,which can transform to asymmet...Soliton molecules(SMs)of the(2+1)-dimensional generalized KonopelchenkoDubrovsky-Kaup-Kupershmidt(gKDKK)equation are found by utilizing a velocity resonance ansatz to N-soliton solutions,which can transform to asymmetric solitons upon assigning appropriate values to some parameters.Furthermore,a double-peaked lump solution can be constructed with breather degeneration approach.By applying a mixed technique of a resonance ansatz and conjugate complexes of partial parameters to multisoliton solutions,various kinds of interactional structures are constructed;There include the soliton molecule(SM),the breather molecule(BM)and the soliton-breather molecule(SBM).Graphical investigation and theoretical analysis show that the interactions composed of SM,BM and SBM are inelastic.展开更多
Two nonlocal Alice–Bob Sawada–Kotera(ABSK) systems, accompanied by the parity and time reversal invariance are studied. The Lax pairs of two systems are uniformly written out in matrix form. The periodic waves, mult...Two nonlocal Alice–Bob Sawada–Kotera(ABSK) systems, accompanied by the parity and time reversal invariance are studied. The Lax pairs of two systems are uniformly written out in matrix form. The periodic waves, multiple solitons, and soliton molecules of the ABSK systems are obtained via the bilinear method and the velocity resonant mechanism. Though the interactions among solitons are elastic, the interactions between soliton and soliton molecules are not elastic.In particular, the shapes of the soliton molecules are changed explicitly after interactions.展开更多
基金Supported by the National Natural Science Foundation of China(12001424)the Natural Science Basic Research Program of Shaanxi Province(2021JZ-21)the Fundamental Research Funds for the Central Universities(2020CBLY013)。
文摘Soliton molecules(SMs)of the(2+1)-dimensional generalized KonopelchenkoDubrovsky-Kaup-Kupershmidt(gKDKK)equation are found by utilizing a velocity resonance ansatz to N-soliton solutions,which can transform to asymmetric solitons upon assigning appropriate values to some parameters.Furthermore,a double-peaked lump solution can be constructed with breather degeneration approach.By applying a mixed technique of a resonance ansatz and conjugate complexes of partial parameters to multisoliton solutions,various kinds of interactional structures are constructed;There include the soliton molecule(SM),the breather molecule(BM)and the soliton-breather molecule(SBM).Graphical investigation and theoretical analysis show that the interactions composed of SM,BM and SBM are inelastic.
文摘Two nonlocal Alice–Bob Sawada–Kotera(ABSK) systems, accompanied by the parity and time reversal invariance are studied. The Lax pairs of two systems are uniformly written out in matrix form. The periodic waves, multiple solitons, and soliton molecules of the ABSK systems are obtained via the bilinear method and the velocity resonant mechanism. Though the interactions among solitons are elastic, the interactions between soliton and soliton molecules are not elastic.In particular, the shapes of the soliton molecules are changed explicitly after interactions.
