| Abstract: |
| In this talk, we study the real and complex modified coupled dispersionless
(CD) equations, the real and complex modified short pulse (SP) equations geometrically
and algebraically. From the geometric point of view, we first establish the
link of the motions of space curves to the real and complex modified CD equations,
then to the real and complex modified SP equations via hodograph transformations.
The integrability of these equations are confirmed by constructing their Lax
pairs geometrically. The $N$-soliton solutions in the form of determinants for the modified SP
equation and two-component modified SP equation are provided. |
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