Two(3+1)-dimensional shallow water wave equations are studied by using residual symmetry and the consistent Riccati expansion(CRE) method. Through localization of residual symmetries, symmetry reduction solutions of t...Two(3+1)-dimensional shallow water wave equations are studied by using residual symmetry and the consistent Riccati expansion(CRE) method. Through localization of residual symmetries, symmetry reduction solutions of the two equations are obtained. The CRE method is applied to the two equations to obtain new B?cklund transformations from which a type of interesting interaction solution between solitons and periodic waves is generated.展开更多
A nonlocal coupled Kadomtsev–Petviashivili(ncKP) system with shifted parity(P_(s)^(x)) and delayed time reversal(T_(d)) symmetries is generated from the local coupled Kadomtsev–Petviashivili(cKP) system. By introduc...A nonlocal coupled Kadomtsev–Petviashivili(ncKP) system with shifted parity(P_(s)^(x)) and delayed time reversal(T_(d)) symmetries is generated from the local coupled Kadomtsev–Petviashivili(cKP) system. By introducing new dependent variables which have determined parities under the action of P_(s)^(x)T_(d)^(d), the ncKP is transformed to a local system. Through this way, multiple even number of soliton solutions of the ncKPI system are generated from N-soliton solutions of the c KP system, which become breathers by choosing appropriate parameters. The standard Lie symmetry method is also applied on the ncKPII system to get its symmetry reduction solutions.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11975156 and 12175148)。
文摘Two(3+1)-dimensional shallow water wave equations are studied by using residual symmetry and the consistent Riccati expansion(CRE) method. Through localization of residual symmetries, symmetry reduction solutions of the two equations are obtained. The CRE method is applied to the two equations to obtain new B?cklund transformations from which a type of interesting interaction solution between solitons and periodic waves is generated.
基金supported by the National Natural Science Foundation of China under Grant Nos.12175148,11975156.
文摘A nonlocal coupled Kadomtsev–Petviashivili(ncKP) system with shifted parity(P_(s)^(x)) and delayed time reversal(T_(d)) symmetries is generated from the local coupled Kadomtsev–Petviashivili(cKP) system. By introducing new dependent variables which have determined parities under the action of P_(s)^(x)T_(d)^(d), the ncKP is transformed to a local system. Through this way, multiple even number of soliton solutions of the ncKPI system are generated from N-soliton solutions of the c KP system, which become breathers by choosing appropriate parameters. The standard Lie symmetry method is also applied on the ncKPII system to get its symmetry reduction solutions.
