相关论文: Non-orthogonally transitive $G_2$ spike solution

For the nonlinear matrix equations arising in the analysis of M/G/1-type and GI/M/1-type Markov chains, the minimal nonnegative solution $G$ or $R$ can be found by Newton-like methods. Recently a fast Newton's iteration is proposed in…

The nested off-diagonal Bethe ansatz is generalized to study the quantum spin chain associated with the $SU_q(3)$ R-matrix and generic integrable non-diagonal boundary conditions. By using the fusion technique, certain closed operator…

We show how one can systematically construct vacuum solutions to Einstein field equations with $D-2$ commuting Killing vectors in $D>4$ dimensions. The construction uses Einstein-scalar field seed solutions in 4 dimensions and is performed…

The method of point transformation of the functions and variables for construction of particular solutions of the Equations of Nonstationary Transonic Gas Flows is used.

The Gram-Schmidt Process (GSP) is used to convert a non-orthogonal basis (a set of linearly independent vectors, matrices, etc) into an orthonormal basis (a set of orthogonal, unit-length vectors, bi or tri dimensional matrices). The…

The graded off-diagonal Bethe ansatz method is proposed to study supersymmetric quantum integrable models (i.e., quantum integrable models associated with superalgebras). As an example, the exact solutions of the $SU(2|2)$ vertex model with…

A linear group G on a finite vector space V, (that is, a subgroup of GL(V)) is called (1/2)-transitive if all the G-orbits on the set of nonzero vectors have the same size. We complete the classification of all the (1/2)-transitive linear…

The $so(5)$ (i.e., $B_2$) quantum integrable spin chains with both periodic and non-diagonal boundaries are studied via the off-diagonal Bethe Ansatz method. By using the fusion technique, sufficient operator product identities (comparing…

In this paper, we study the existence of rotating and traveling-wave solutions for the generalized surface quasi-geostrophic (gSQG) equation. The solutions are obtained by maximization of the energy over the set of rearrangements of a fixed…

We construct a generalized Darboux transformation (GDT) of a general coupled nonlinear Schr\"{o}dinger (GCNLS) system. Using GDT method we derive a recursive formula and present determinant representations for N-th order rogue wave solution…

The set of benchmark solutions used in the thermal radiative transfer community suffer some coverage gaps, in particular nonlinear, non-equilibrium problems. Also, there are no non-equilibrium, optically thick benchmarks. These shortcomings…

A nonconforming $P_2$ finite element is constructed by enriching the conforming $P_2$ finite element space with seven $P_2$ nonconforming bubble functions (out of fifteen such bubble functions on each tetrahedron). This spacial…

With every nontrivial connected algebraic group $G$ we associate a positive integer ${\rm gtd}(G)$ called the generic transitivity degree of $G$ and equal to the maximal $n$ such that there is a nontrivial action of $G$ on an irreducible…

In the framework of the resolvent approach it is introduced a so called twisting operator that is able, at the same time, to superimpose \`a la Darboux $N$ solitons to a generic smooth decaying potential of the Nonstationary Schr\"odinger…

A nonlocal derivative nonlinear Schrodinger equation is introduced. By constructing its basic Darboux transformations of degrees one and two, the explicit expressions of new solutions are derived from seed solutions by Darboux…

The nested off-diagonal Bethe ansatz method is proposed to diagonalize multi-component integrable models with generic integrable boundaries. As an example, the exact solutions of the su(n)-invariant spin chain model with both periodic and…

This paper studies the Poisson equation for the $G_2$-Laplacian on 3-forms on the 7-sphere that are invariant under a transitive group action. We establish the existence and uniqueness of $G$-invariant solutions for $G=SU(4),\: Spin(7),\:…

In this second paper on the method of deriving linearizing transformations for nonlinear ODEs, we extend the method to a set of two coupled second order nonlinear ODEs. We show that besides the conventional point, Sundman and generalized…

We propose a modification of the standard inverse scattering transform for the focusing nonlinear Schr\"odinger equation (also other equations by natural generalization) formulated with nonzero boundary conditions at infinity. The purpose…

Let $G$ be a permutation group on a finite set $\Omega$. The $k$-closure $G^{(k)}$ of the group $G$ is the largest subgroup of $\operatorname{Sym}(\Omega)$ having the same orbits as $G$ on the $k$-th Cartesian power $\Omega^k$ of $\Omega$.…