We develop a Fourier–Galerkin spectral technique for computing the solutions of type of interacting localized waves. To this end, a special complete orthonormal system of functions in L2(−∞,∞) is used and a time-stepping algorithm implementing the spectral method is developed. The rate...

Quantification of baseflow to drainage ditches is essential in understanding flow dynamics in a watershed. The mass balance estimation for a stream section may not give an accurate measure of the baseflow during low-flow periods due to the lack of accuracy in flow measurements in the flumes....

Travelling wave solutions for the Boussinesq-double sine-Gordon (B-sine-Gordon) equation, the Boussinesq-double sinh-Gordon equation (B-sinh-Gordon), and the Boussinesq-Liouville (BL) equation are formally derived. The approach rests mainly on the variable separated ODE method. Distinct sets of...

This paper presents analytical solution of one-dimensional linearized Boussinesq equation characterizing unsteady groundwater flow in an unconfined aquifer, overlying an impervious downward sloping bed. At one end, the aquifer is in contact with a constant water level and at the other end; water...

It is shown that if a new bilinear Bäcklund transformation to Boussinesq equation has been reduced by the gauge transformation, it always has another set of new N-soliton solution by performing an appropriate limiting procedure on the already known ones.

Using a long wave expansion we study the asymptotic solutions near a critical point of a multi-anticipative car-following model. A suitable rescaling of the variables then yields a modified Korteweg–de Vries (MKdV) equation with higher order corrections. An equation of this general form has...

We analyze a system of reacting elements harmonically coupled to nearest neighbors in the continuum limit. An analytic solution is found for traveling waves. The procedure is used to find oscillatory as well as solitary waves. A comparison is made between exact solutions and solutions of the...