Full Symmetry Groups and Exact Solutions towhere , , , , and are functions of (, , ) to be determined by requiring (, , ) to satisfy the same (2+1)- dimensional GKP equation as V(, , ) under the transfor- mation {V, , , } → {, , , }GKP Equations...
where a, b and c can be any one of z, x and o. let us temporarily call it the rlll relation of type abc. the main result of this paper is the explicit solution r for types zzz, ozz, zzo, zoz, ooz, zoo, ozo, ooo, xxz, zxx and xzx. they turn out to be unique up to...
to a Transient Condition • Advanced Wave Loading • TOPOLOGY OPTIMIZATION Structural Optimization ••• Modal Optimization ••• Thermal Loads ••• Inertial Loads Optimized Design Validation Manufacturing Constraints Stress constraints Symmetry Lattice Optimization Overhang/Additive ...
we introduce the notion of a twisting pair for h such that the zhang twist of h by such a pair is a 2-cocycle twist. we use twisting pairs to describe twists of manin’s universal quantum groups associated with quadratic algebras and provide ...
The methods involve, first, reduction of the Schrdinger equations to group-invariant semilinear complex 2nd order ordinary differential equations (ODEs) with respect to an optimal set of one-dimensional point symmetry groups, and second, use of inherited symmetries, hidden symmetries, and conditional ...
method is developed to find finite symmetry groups of nonlinear mathematical physicssystems.Applying the modified direct method to the well-known (2+1)-dimensional BKP equation we get its symmetry.Furthermore,the exact solutions of (2+1)-dimensional BKP equation are obtained through symmetry ...
We have analysed a large class of nonlinear KdV type and related generalisations like vector and beta model equations using variational and/or symmetry methods. These lead to exact solutions like travelling wave, soliton and other similarity solutions. Acknowledgement AHK thanks the HEC of Pakistan ...
Keywords: optimal homotopy asymtotic method; dynamical system; symmetries; Hamilton–Poisson realization; asymptotic behaviors MSC: 37B65; 37C79; 65H20; 37J06; 37J35; 65L991. Introduction In order to understand the threshold between the disappearance of disease and epidemic outbreak, mathematical ...
In this paper, we prove that there are at most four solutions in positive integers (x,y,z) to the equation kax+lby=cz and at most two solutions when 2∤(u(l/k)), where u(m) is the least positive integer t with mt≡1(modc). Video For a video summary of this paper, please...
The aim of this review is to present a comprehensive overview of the feasibility of using transparent neural interfaces in multimodal in vivo experiments on the central nervous system. Multimodal electrophysiological and neuroimaging approaches hold great potential for revealing the anatomical and functional...