The adiabatic decay of different types of internal wave solitons caused by the Earth’ rotation is considered within the framework of the Gardner–Ostrovsky equation. The governing equation describing such processes includes quadratic and cubic nonlinear terms, as well as the Boussinesq and Coriolis dispersions. It is shown that at the early stage of evolution solitons gradually decay under the i...

Integrability of the quantum Boussinesq equation for c = −2 is demonstrated by giving a recursive algorithm for generating explicit expressions for the infinite number of commuting charges based on a reduction of the W∞ algebra. These charges exist for all spins s ≥ 2. Likewise, reductions of the W∞/2 and W(1+∞)/2 algebras yield the commuting quantum charges for the quantum KdV equation at c = ...

In this article, we establish new traveling wave solutions for the loaded Boussinesq equation and modified by functional variable method. The performance of method is reliable effective gives exact solitary periodic its modifications. obtained via are expressed hyperbolic functions trigonometric functions. graphical representations some demonstrated to better understand their physical features,...

In order to investigate corrections to the common KdV approximation to long waves, we derive modulation equations for the evolution of long wavelength initial data for a Boussinesq equation. The equations governing the corrections to the KdV approximation are explicitly solvable and we prove estimates showing that they do indeed give a significantly better approximation than the KdV equation al...

This paper obtains the soliton solutions to the Boussinesq equation with the effect of surface tension being taken into account. The power law nonlinearity is considered. Three integration tools are adopted in order to extract the soliton solutions. They are the traveling wave hypothesis, ansatz method and the semi-inverse variational principle. Finally, the Lie symmetry approach is adopted to ...

Wronskian determinants are used to construct exact solution to integrable equations. The crucial steps are to apply Hirota’s bilinear forms and explore linear conditions to guarantee the Plücker relations. Upon solving the linear conditions, the resultingWronskian formulations bring solution formulas, which can yield solitons, negatons, positions and complexitons. The solution process is illust...

We show that a type of linear superposition principle works for several nonlinear differential equations. Using this approach, we find periodic solutions of the Kadomtsev-Petviashvili (KP) equation, the nonlinear Schrödinger (NLS) equation, the λφ4 model, the sine-Gordon equation and the Boussinesq equation by making appropriate linear superpositions of known periodic solutions. This unusual pr...