On the solutions of the dKP equation: the nonlinear Riemann Hilbert problem, longtime behaviour, implicit solutions and wave breaking
نویسندگان
چکیده
منابع مشابه
N ov 2 00 7 On the solutions of the dKP equation : nonlinear Riemann Hilbert problem , longtime behaviour , implicit solutions and wave breaking
We have recently solved the inverse scattering problem for oneparameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations in multidimensions, including the second heavenly equation of Plebanski and the dispersionless Kadomtsev Petviashvili (dKP) equation. We showed, in particu...
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We have recently solved the inverse spectral problem for oneparameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations in multidimensions, including the second heavenly equation of Plebanski and the dispersionless Kadomtsev Petviashvili (dKP) equation, arising as commutation ...
متن کاملar X iv : 0 70 7 . 18 02 v 2 [ nl in . S I ] 1 3 Ju l 2 00 7 On the solutions of the dKP equation :
We have recently solved the inverse scattering problem for oneparameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations in multidimensions, including the second heavenly equation of Plebanski and the dispersionless Kadomtsev Petviashvili (dKP) equation. We showed, in particu...
متن کاملN ov 2 00 8 The dispersionless 2 D Toda equation : dressing , Cauchy problem , longtime behaviour , implicit solutions and wave breaking
We have recently solved the inverse spectral problem for oneparameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations in multidimensions, including the second heavenly equation of Plebanski and the dispersionless Kadomtsev Petviashvili (dKP) equation, arising as commutation ...
متن کاملTwistor Solutions of the dKP Equation ∗
The factorization problem for the group of canonical transformations close to the identity and the corresponding twistor equations for an ample family of canonical variables are considered. A method to deal with these reductions is developed for the construction classes of nontrivial solutions of the dKP equation.
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2008
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/41/5/055204