Three (2 + 1)-dimensional equations—Burgers equation, cylindrical Burgers equation and spherical Burgers equation, have been reduced to the classical Burgers equation by different transformation of variables respectively. The decay mode solutions of the Burgers equation have been obtained by using the extended G G ′       -expansion method, substituting the solutions obtained into the cor...

We describe a kinetic theory for shock clustering in scalar conservation laws with random initial data. Our main discovery is that for a natural class of random data the shock clustering is described by a completely integrable Hamiltonian system. Thus, the problem is in a precise sense exactly solvable. Our results have implications in other areas: mathematical physics (limits of shell models o...

Unsteady oscillatory flow of generalized Burgers’ fluid in a circular channel tube in the porous medium is investigated under the influence of time-dependent trapezoidal pressure gradient given by an infinite Fourier series. An exact analytical expression for the solution for the fluid velocity and the shear stress are recovered by using the similarity arguments together with the integral trans...

We study the scalar conservation law with a noisy non-linear source, viz., ut +f(u)x = h(u; x; t) + g(u)W (t), where W (t) is white noise in the time variable, and we analyse the Cauchy problem for this equation where the initial data are assumed to be deterministic. A method is proposed to construct approximate weak solutions, and we then show that this yields a convergent sequence. This seque...

By means of modified extended direct algebraic (MEDA) method the multiple exact complex solutions of some different kinds of nonlinear partial differential equations are presented and implemented in a computer algebraic system. New complex solutions for nonlinear equations such as one-dimensional Burgers, KDV-Burgers, coupled Burgers and twodimensional Burgers’ equations are obtained.

 Microbiological, chemical and sensory changes of fish burgers prepared from deep flounder (Pseudorhombus elevatus) and brushtooth lizardfish (Saurida undosquamis) were determined during storage at -18ºC for 5 months. Microbiological counts were including total plate count (TPC), total coliform (TC), Staphylococcus aureus, Psychotropic and Escherichia coli decreased throughout the frozen storag...

Keywords: Compact schemes Finite difference method Burgers' equation Low-storage Runge–Kutta scheme a b s t r a c t A numerical solution of the one-dimensional Burgers' equation is obtained using a sixth-order compact finite difference method. To achieve this, a tridiagonal sixth-order compact finite difference scheme in space and a low-storage third-order total variation diminishing Runge–Kutt...

Waves with constant, nonzero linearized frequency form an interesting class of nondispersive waves whose properties differ from those of nondispersive hyperbolic waves. We propose an inviscid Burgers-Hilbert equation as a model equation for such waves, and give a dimensional argument to show that it models Hamiltonian surface waves with constant frequency. Using the method of multiple scales, w...