6533b861fe1ef96bd12c44b7
RESEARCH PRODUCT
Three dimensional reductions of four-dimensional quasilinear systems
Nikola StoilovMaxim V. PavlovMaxim V. Pavlovsubject
Nonlinear Sciences - Exactly Solvable and Integrable SystemsIntegrable system010102 general mathematicsInverse scattering[ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]FOS: Physical sciencesStatistical and Nonlinear PhysicsDispersionFirst order01 natural sciencesNonlinear Sciences::Exactly Solvable and Integrable SystemsMathematical methods[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]0103 physical sciences010307 mathematical physicsExactly Solvable and Integrable Systems (nlin.SI)0101 mathematicsTranscendental number theoryNonlinear Sciences::Pattern Formation and SolitonsMathematical PhysicsMathematicsMathematical physicsdescription
In this paper we show that integrable four dimensional linearly degenerate equations of second order possess infinitely many three dimensional hydrodynamic reductions. Furthermore, they are equipped infinitely many conservation laws and higher commuting flows. We show that the dispersionless limits of nonlocal KdV and nonlocal NLS equations (the so-called Breaking Soliton equations introduced by O.I. Bogoyavlenski) are one and two component reductions (respectively) of one of these four dimensional linearly degenerate equations.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-11-01 |