Related papers: Elliptic solutions to a generalized BBM equation
In this paper, a simple, robust, fast and effective method based on the conserved quantities is developed to approximate and analyse the shape, structure and interaction characters of the solitary waves described by the Benjamin-Bona-Mahony…
We obtain in terms of the Weierstrass elliptic $\wp-$function, sigma function, and zeta function an explicit parametrized solution of a particular nonlinear, ordinary differential equation. This equation includes, in special cases,…
The paper deals with a problem of asymptotic soliton like solutions to the Benjamin-Bona-Mahony (BBM) equaion with a small parameter at the highest derivative and variable coefficients depending on the variables $x$, $t$ as well as a small…
We present a new general, complete closed-form solution of the Stark problem in terms of Weierstrass elliptic and related functions. With respect to previous treatments of the problem, our analysis is exact and valid for all values of the…
The initial- and boundary-value problem for the Benjamin-Bona-Mahony (BBM) equation is studied in this paper. The goal is to understand the periodic behavior (termed as eventual periodicity) of its solutions corresponding to periodic…
The singularities that arise in elliptic boundary value problems are treated locally by a singular function boundary integral method. This method extracts the leading singular coefficients from a series expansion that describes the local…
A simple and general approach for calculating the elliptic finite-gap solutions of the Korteweg-de Vries (KdV) equation is proposed. Our approach is based on the use of the finite-gap equations and the general representation of these…
New problem is studied that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. Method is discussed to construct nonlinear ordinary differential equations with exact solutions. Main…
We develop a variational regularisation framework that enables analytical solutions of the stationary de~Broglie--Bohm wave equation. The formulation begins with a Fisher-information-augmented action functional for the probability density…
Some classes of the rational, periodic and solitary wave solutions for the Burgers hierarchy are presented. The solutions for this hierarchy are obtained by using the generalized Cole - Hopf transformation.
The mathematical pendulum is traditionally solved using a Jacobi elliptic functions. We solve it here using the Weierstrass elliptic function. Every initial condition of the pendulum produces an elliptic curve and a point which by the…
The analytic general solutions for the complex field envelopes are derived using Weierstrass elliptic functions for two and three mode systems of differential equations coupled via quadratic $\chi_2$ type nonlinearity as well as two mode…
Jacobian elliptic travelling wave solutions for a new Hamiltonian amplitude equation determining some instabilities of modulated wave train are obtained. By mere variation of the Jacobian elliptic parameter $k^2$ from zero to one, these…
In this paper, we obtain a uniform $W^{2,\varepsilon}$-estimate of solutions to the fully nonlinear uniformly elliptic equations on Riemannian manifolds with a lower bound of sectional curvature using the ABP method.
The paper deals with a problem of asymptotic step-like solutions to the Burgers' equation with variable coefficients and a small parameter. By means of the non-linear WKB method, the algorithm of constructing these asymptotic solutions is…
In this note, we establish the interior $BMO$ regularity of weak solutions to uniformly elliptic equations in divergence form. Moreover, the assumptions on the coefficients are nearly optimal.
Analysis of the generalized Weierstrass-Enneper system includes the estimation of the degree of indeterminancy of the general analytic solution and the discussion of the boundary value problem. Several different procedures for constructing…
The Lattice Boltzmann Method (LBM), e.g. in [ 1] and [2 ], can be interpreted as an alternative method for the numerical solution of partial differential equations. Consequently, although the LBM is usually applied to solve fluid flows, the…
A Weierstrass type projective Riccati equation expansion method is proposed by using the Weierstrass elliptic function solutions of the projective Riccati equations and the conversion formulas which transform the Weierstrass elliptic…
The generalized fractional Benjamin-Bona-Mahony (gfBBM) equation models the propagation of small amplitude long unidirectional waves in a nonlocally and nonlinearly elastic medium. The equation involves two fractional terms unlike the…