In this paper, we present a new method for computing approximate geodesic distances. We introduce the wave method for approximating geodesic distances from a point on a manifold mesh. Our method involves the solution of two linear systems of equations. One system of equations is solved repeatedly to propagate the wave on the entire mesh, and one system is solved once after wave propagation is c...

Generalized solitary waves arise in many physical systems, including water waves with surface tension and multi-layered fluids [7,19,21,22]. They are nonlinear long waves consisting of a localized central core and periodic non-decaying oscillations extending to infinity. They arise whenever there is a resonance between a linear long wave speed of one wave mode in the system and a wave speed wit...

In this work, we extended the application of “the modified reductive perturbation method” to long water waves and obtained the governing equations of Korteweg – de Vries (KdV) hierarchy. Seeking localized travelling wave solutions to these evolution equations we have determined the scale parameter g1 so as to remove the possible secularities that might occur. To indicate the effectiveness and t...

Under special conditions an approximate wave front solution to a system of nonlinear reaction-diffusion type equations is obtained. An assumption of fast kinetics permits the system to be reformulated as a single nonlinear differential-integral equation of convolution type. If the convolution kernel has the form of a mollifier then the convolution is localized to obtain an infinite system of di...

A new integral transform method for regularized long-wave (RLW) models having fractional-order is presented in this study. Although analytical approaches are challenging to apply such models, semianalytical or numerical techniques have received much attention the literature. We propose a technique combining transformation, Elzaki (ET), and it equations The RLW describe ion-acoustic waves plasma...

in the present work properties of rossby and inertia gravity waves are investigated based on proper orthogonal decomposition (pod) functions. the pod functions are constructed using analytical, experimental or numerical data recorded as snapshots. the pod basis can be carried out to make a reduced order model by galerkin projection of governing equations onto these functions. in this paper, the...

The water wave equations of ideal free–surface fluid mechanics are a fundamental model of open ocean movements with a surprisingly subtle well–posedness theory. In consequence of both theoretical and computational difficulties with the full water wave equations, various asymptotic approximations have been proposed, analysed and used in practical situations. In this essay, we establish the well–...

In this paper a set of approximate equations is derived which is applicable to very nonadiabati c, nondissipative, buoyant flows of a perfect gas. The flows are assumed to be generated by a heat source in which the heat is added slowly. The study is motivated by the occurrence of such f] ows in fires. There, the time scale associated with the fire growth and resultant f]uid moti on is usually l...