Abstract
The main concern of this paper is to apply the modified double Laplace decomposition method to a singular generalized modified linear Boussinesq equation and to a singular nonlinear Boussinesq equation. An a priori estimate for the solution is also derived. Some examples are given to validate and illustrate the method.
Highlights
One and higher dimensional Boussinesq equations are generally used in coastal and ocean engineering, modelling tidal oscillations and tsunami wave modelling. These equations are classified as hyperbolic equations, like nonlinear shallow water equations, and they were originally derived as a model for water waves
The purpose of the main result of this work is to use the modified double Laplace decomposition method for solving a singular generalized modified linear Boussinesq equation and a singular nonlinear Boussinesq equation
We obtain an a priori estimate for the solution and we provide some examples to validate and illustrate the modified double Laplace decomposition method
Summary
One and higher dimensional Boussinesq equations are generally used in coastal and ocean engineering, modelling tidal oscillations and tsunami wave modelling. Where x, t > 0 and p, s are complex values, and further double Laplace transform of the first order partial derivatives for a function u is given by. In the rectangle Q = (0, 1) × (0, T ), T < ∞, we consider an initial boundary value problem for the singular generalized improved modified linear Boussinesq equation with damping and with. We obtain an a priori estimate for the solution of problem (14)–(16) and use the modified double Laplace decomposition method for solving it. By discarding the last two terms in the left-hand side of (26) and taking the upper bound for both sides with respect to τ over [0, T ] of the obtained inequality, we obtain the following a priori estimate for the solution of the posed problem (14)–(16)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
