Solitons and the Inverse Scattering Transform
A study of the inverse scattering transform and its application to problems of nonlinear dispersive waves that arise in fluid dynamics, plasma physics, nonlinear optics, particle physics, crystal lattice theory, nonlinear circuit theory and other areas.
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Ablowitz action-angle variables algebra amplitude analytic applied asymptotic solution Backlund transformation boundary conditions coefficients conservation laws consider constant corresponding decay defined derivation differential equations discrete eigenvalues discussed dispersion relation eigenfunctions energy integral example expansion finite Fluid Mech Fourier transform function given group velocity Hamiltonian Hence infinite initial data interaction internal waves inverse scattering inverse scattering transform J—oo Kadomtsev-Petviashvili equation Kaup KdV equation Korteweg-deVries equation Kruskal lattice Lett Lie algebra linear integral equation linearized dispersion relation linearized problem long waves Manakov Math method mKdV N-soliton Newell nonlinear evolution equations nonlinear Schrodinger equation obtained ODE's ordinary differential equations P-type Painleve perturbation Phys potential pseudopotential satisfies Satsuma scattering data scattering problem Segur Shabat Show sine-Gordon equation singularity solitary waves soliton solutions solved by 1ST surface waves theory unstable uxxx vanish variables water waves yields zero