TY - JOUR

T1 - Integrable equations in 2 + 1 dimensions: deformations of dispersionless limits

AU - Ferapontov, Eugene

AU - Moro, Antonio

AU - Novikov, Vladimir

PY - 2009

Y1 - 2009

N2 - We classify integrable third-order equations in 2 + 1 dimensions which generalize the examples of Kadomtsev–Petviashvili, Veselov–Novikov and Harry Dym equations. Our approach is based on the observation that dispersionless limits of integrable systems in 2 + 1 dimensions possess infinitely many multi-phase solutions coming from the so-called hydrodynamic reductions. In this paper, we adopt a novel perturbative approach to the classification problem. Based on the method of hydrodynamic reductions, we first classify integrable quasilinear systems which may (potentially) occur as dispersionless limits of soliton equations in 2 + 1 dimensions. To reconstruct dispersive deformations, we require that all hydrodynamic reductions of the dispersionless limit be inherited by the corresponding dispersive counterpart. This procedure leads to a complete list of integrable third-order equations, some of which are apparently new.

AB - We classify integrable third-order equations in 2 + 1 dimensions which generalize the examples of Kadomtsev–Petviashvili, Veselov–Novikov and Harry Dym equations. Our approach is based on the observation that dispersionless limits of integrable systems in 2 + 1 dimensions possess infinitely many multi-phase solutions coming from the so-called hydrodynamic reductions. In this paper, we adopt a novel perturbative approach to the classification problem. Based on the method of hydrodynamic reductions, we first classify integrable quasilinear systems which may (potentially) occur as dispersionless limits of soliton equations in 2 + 1 dimensions. To reconstruct dispersive deformations, we require that all hydrodynamic reductions of the dispersionless limit be inherited by the corresponding dispersive counterpart. This procedure leads to a complete list of integrable third-order equations, some of which are apparently new.

U2 - 10.1088/1751-8113/42/34/345205

DO - 10.1088/1751-8113/42/34/345205

M3 - Article

SN - 1751-8113

VL - 42

SP - 345205

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 34

ER -