<Abstract>We develop the generalized conditional symmetry (GCS) approach to solve the problem of dimensional reduction of Cauchy problems for the KdV-type equations.We characterize these equations that admit cer...<Abstract>We develop the generalized conditional symmetry (GCS) approach to solve the problem of dimensional reduction of Cauchy problems for the KdV-type equations.We characterize these equations that admit certain higher- order GCSs and show the main reduction procedure by some examples.The obtained reductions cannot be derived within the framework of the standard Lie approach.展开更多
We exploit higher-order conditional symmetry to reduce initial-value problems for evolution equations toCauchy problems for systems of ordinary differential equations (ODEs).We classify a class of fourth-order evoluti...We exploit higher-order conditional symmetry to reduce initial-value problems for evolution equations toCauchy problems for systems of ordinary differential equations (ODEs).We classify a class of fourth-order evolutionequations which admit certain higher-order generalized conditional symmetries (GCSs) and give some examples to showthe main reduction procedure.These reductions cannot be derived within the framework of the standard Lie approach,which hints that the technique presented here is something essential for the dimensional reduction of evolu tion equations.展开更多
基金supported by National Natural Science Foundation of China under Grant Nos.10447007 and 10671156the Natural Science Foundation of Shaanxi Province of China under Grant No.2005A13
文摘<Abstract>We develop the generalized conditional symmetry (GCS) approach to solve the problem of dimensional reduction of Cauchy problems for the KdV-type equations.We characterize these equations that admit certain higher- order GCSs and show the main reduction procedure by some examples.The obtained reductions cannot be derived within the framework of the standard Lie approach.
基金National Natural Science Foundation of China under Grant Nos.10447007 and 10671156the Natural Science Foundation of Shaanxi Province of China under Grant No.2005A13
文摘We exploit higher-order conditional symmetry to reduce initial-value problems for evolution equations toCauchy problems for systems of ordinary differential equations (ODEs).We classify a class of fourth-order evolutionequations which admit certain higher-order generalized conditional symmetries (GCSs) and give some examples to showthe main reduction procedure.These reductions cannot be derived within the framework of the standard Lie approach,which hints that the technique presented here is something essential for the dimensional reduction of evolu tion equations.
