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A classification of pseudospherical surface equations of type \(u_ t=u_{xxx}+G(u,u_ x,u_{xx}\)). (English) Zbl 0755.35121

Summary: The equations of type \(u_ t=u_{xxx}+G(u,u_ x,u_{xx})\) which describe \(\eta\)-pseudospherical surfaces are characterized. A new class of such equations is obtained. This class together with the Korteweg-de Vries (KdV) equation, the modified Korteweg-de Vries (MKdV) equation, and the linear equation completes the classification.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
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[1] DOI: 10.1002/sapm198674155 · Zbl 0605.35080 · doi:10.1002/sapm198674155
[2] DOI: 10.1002/sapm1987772103 · Zbl 0642.35017 · doi:10.1002/sapm1987772103
[3] DOI: 10.1002/sapm1989813221 · Zbl 0696.35111 · doi:10.1002/sapm1989813221
[4] DOI: 10.1002/sapm1974534249 · Zbl 0408.35068 · doi:10.1002/sapm1974534249
[5] DOI: 10.1063/1.528727 · Zbl 0711.35085 · doi:10.1063/1.528727
[6] DOI: 10.1137/0142025 · Zbl 0488.76099 · doi:10.1137/0142025
[7] DOI: 10.1007/BF00046886 · Zbl 0683.58025 · doi:10.1007/BF00046886
[8] DOI: 10.1063/1.528020 · Zbl 0695.35038 · doi:10.1063/1.528020
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