Method of lines solutions of the extended Boussinesq equations

Method of lines solutions of the parabolic inverse problem with an overspecification at a point

“…This technique has the broad applicability to physical and chemical systems modeled by PDEs. The models that include the solution of mixed systems of algebraic equations, the resolution of steep moving fronts, parameter estimation and optimal control, other problems such as delay differential equations [34], two-dimensional sine-Gordon equation [2], the Boussinesq equation [3], coupled generalized Kortoweg de Vries and quintic regularized long wave equations [32], the Nwogu's one-dimensional extended Boussinesq equation [31], partial differential equation describing nonlinear wave phenomena, e.g., a fully nonlinear third order Korteweg-de Vries (KdV) equation, the fourth-order Boussinesq equation, the fifth order Kaup-Kupershmidt equation and an extended KdV5 equation [39], non-linear inverse heat conduction problem [42], interface problem [33], multi-component atmospheric pollutant propagation model with pollutants phase transformation consideration [28], a Bingham problem in cylindrical pipes [43], a mathematical model for capillary formation [29,36], 3-D transient radiative transfer equation [1], elliptic partial differential equations which describe steady-state mass and energy transport in solids [41] and many other physical problems. Some of the options available for time integration when using a moving grid MOL code is surveyed in [11].…”

Numerical Solutions of the Forced Perturbed Korteweg-De Vries Equation With Variable Coefficients

“…MOL has been widely used to solve the nonlinear evolution equations such as Korteweg-de Vries (KdV) equation [8], extended nonlinear KdV equation, good Boussinesq equation, fifth-order KaupKupershmidt equation and an extended fifth-order Korteweg-de Vries (KdV5) equation [9], delay differential equations [10], two-dimensional sine-Gordon equation [11], the Nwogu one-dimensional extended Boussinesq equation [12].…”

Solitary wave solutions of the one-dimensional Boussinesq equations

“…Due to the importance of the subject, a lot of research papers have been devoted to the subject not only from the theoretical point of view, see for example Chen [4] and [13][14][15] Hamdi et al [5,6] but also from the numerical point of view. Numerous numerical solutions to Boussinesq-type equations in one-dimension have been given among others by Bratsos [7,8] and Hamdi et al [9]. In this work, we derive analytical solitary wave solutions of the one-dimensional Boussinesq equations, as those which were introduced by Peregrine [1] and were modified by Madsen et al [2] in the case of waves relatively long, with small amplitudes, in water of varying depth.…”