An improved theory of long waves on water surface. (English. Russian original) Zbl 0881.76016

J. Appl. Math. 61, No. 2, 177-182 (1997); translation from Prikl. Mat. Mekh. 61, No. 2, 184-189 (1997).
The authors consider potential motion of water over infinite horizontal bottom. The water is considered to be an ideal incompressible homogeneous fluid with the depth \(h\) in unperturbed state. By means of Hamiltonian formalism the equations are derived which describe long waves and take into account the second order terms with respect to the small nonlinearity and dispersion parameters. A relationship between the obtained equations and Korteweg-de Vries equations is established, and \(N\)-soliton solutions are described among exact solutions to the Korteweg-de Vries equations.


76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76B25 Solitary waves for incompressible inviscid fluids


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