Given a connected reductive complex algebraic group $G$ and spherical subgroup $H \subset G$, the extended weight monoid $\widehat \Lambda^+_G(G/H)$ encodes $G$-module structures on spaces of global sections all $G$-linearized line bundles $G/H$. Assuming that is semisimple simply $H$ specified by regular embedding in parabolic $P this paper we obtain description via set simple roots $G/H$ toge...

Some new generalized solitary solutions of the Klein–Gordon–Schrödinger equations are obtained using the Exp-function method, which include some known solutions obtained by the F-expansion method and the homogeneous balance method in the open literature as special cases. It is shown that the Exp-function method is a straight, concise, reliable and promising mathematical tool for solving nonline...

We describe several families of wavelets associated to the Galilei group, extended by space and time dilations. The construction follows a general method based on group representations which are square integrable only on a homogeneous space of the underlying group.

In this paper, by the use of the weight coefficients, the transfer formula and the technique of real analysis, an extended multidimensional Hardy-Hilbert-type inequality with a general homogeneous kernel and a best possible constant factor is given. Moreover, the equivalent forms, the operator expressions and a few examples are considered.

Classical homogeneous nucleation theory is extended to nonisothermal conditions through simultaneous cluster mass and energy balances. The transient nucleation of water vapor following a sudden increase in saturation ratio is studied by numerically solving the coupled mass and energy balance equations. The ultimate steady state nucleation rate, considering nonisothermal effects, is found to be ...

in the present work, a hybrid of fourier transform and homotopy perturbation method is developed for solving the non-homogeneous partial differential equations with variable coefficients. the fourier transform is employed with combination of homotopy perturbation method (hpm), the so called fourier transform homotopy perturbation method (fthpm) to solve the partial differential equations. the c...

The aim of this paper is to obtain a set traveling wave solutions for klein –Gorden equation with kerr law non-linearity. More precisely, we apply new path popularized homogeneous balance (HB) method in terms using linear auxiliary equations find the results non-linear klein-Gorden equation, which fundamental approach determine competent solutions. are achieved as integration exponential, hyper...

In this Letter, based on the idea of homogeneous balance (HB) method and with help of MATHEMATICA, we obtain a new auto-Bäcklund transformation for compound KdV-type and compound KdV–Burgers-type equations with nonlinear terms of any order. Then based on the Bäcklund transformation, some solutions for these two equations are derived.  2002 Elsevier Science B.V. All rights reserved.

In this Letter, we study (2 + 1)-dimensional Boussinesq equation and (3 + 1)-dimensional KP equation by using the new generalized transformation in Homogeneous Balance Method (HBM). As a result, many explicit exact solutions, which contain new solitary wave solutions, periodic wave solutions and the combined formal solitary wave solutions and periodic wave solutions, are obtained.  2002 Elsevi...