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The fourth-order nonlinear Schrödinger equation for the envelope of Stokes waves on the surface of a finite-depth fluid
The method of multiple scales is used to derive the fourth-order nonlinear Schrödinger equation (NSEIV) that describes the amplitude modulations of the fundamental harmonic of Stokes waves on theExpand
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A new type of modulation instability of Stokes waves in the framework of an extended NSE system with mean flow
Stokes waves on the surface of a layer of an ideal fluid are studied. The nonlinear Schrodinger equation (NSE) for the envelope of the first harmonic and the equation for zero harmonic are extendedExpand
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The modulational instability of Stokes waves on the surface of finite-depth fluid
Abstract We study the modulational instability of Stokes waves without the traditional assumption as to the movement of a mean flow with the group velocity of the first harmonic. We have shown thatExpand
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Zakharov equations with zeroth harmonic and a new type of modulation instability
It has been shown that the system of Zakharov equations for the amplitudes of the first and zeroth harmonics of the waves on the surface of an ideal liquid describes not only the known type of theExpand
Dispersive terms in the averaged Lagrangian method
Abstract In this paper we develop Whitham's formalism of the averaged Lagrangian in the problem of Stokes waves on the surface of a layer of ideal fluid by taking into account dispersive terms. WeExpand
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High-Order Nonlinear Schrödinger Equation
We consider the high-order nonlinear Schrödinger equation derived earlier by Sedletsky [Ukr. J. Phys. 48(1), 82 (2003)] for the first-harmonic envelope of slowly modulated gravity waves on theExpand
Inclusion of dispersive terms in the averaged Lagrangian method: turning to the complex amplitude of envelope
Whitham’s method of averaged Lagrangian is extended to include dispersive terms on the example of Stokes waves on the surface of a layer of ideal fluid. We derive a Lagrangian with explicitExpand
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The Hamiltonian formalism and a new type of modulation instability
We recently reported the existence of a new type of modulation instability of the waves on the surface of ideal fluid (2006 J. Phys. A: Math. Gen. 39 L529). To this end, we considered the system ofExpand
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