
We study the long time evolution of the solution to the Kortewegde Vries equation with initial data υ ( x ) \upsilon (x) which satisfy \[ lim x → − ∞ υ ( x ) = − 1 , lim x → + ∞ υ ( x ) = 0 \lim \limits _{x \to - \infty } \upsilon (x) = - 1,\qquad \lim \limits _{x \to + \infty } \upsilon (x) = 0 \] We show that as t → ∞ t \to \infty the step emits a wavetrain of solitons which asymptotically have twice the amplitude of the initial step. We derive a lower bound of the number of solitons separated at time t t for t t large.
Inverse problems for PDEs, inverse scattering method, Partial differential equations of mathematical physics and other areas of application, long time asymptotics, Asymptotic behavior of solutions to PDEs, Korteweg-de Vries equation, Scattering theory for PDEs, wavetrain of solitons, Solitary waves for incompressible inviscid fluids
Inverse problems for PDEs, inverse scattering method, Partial differential equations of mathematical physics and other areas of application, long time asymptotics, Asymptotic behavior of solutions to PDEs, Korteweg-de Vries equation, Scattering theory for PDEs, wavetrain of solitons, Solitary waves for incompressible inviscid fluids
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