Zobrazeno 1 - 10
of 132
pro vyhledávání: '"37K10, 37K40"'
Autor:
Naz, Rehana, Hereman, Willy
The Lie-point symmetry method is used to find some closed-form solutions for a constitutive equation modeling stress in elastic materials. The partial differential equation (PDE), which involves a power law with arbitrary exponent n, was investigated
Externí odkaz:
http://arxiv.org/abs/2409.15593
Autor:
Kim, Taegyu, Kwon, Soonsik
We consider soliton resolution for the Calogero--Moser derivative nonlinear Schr\"odinger equation (CM-DNLS). A rigorous PDE analysis of (CM-DNLS) was recently initiated by G\'erard and Lenzmann, who demonstrated its Lax pair structure. Additionally,
Externí odkaz:
http://arxiv.org/abs/2408.12843
Determinant formulas for vacuum expectation values $\langle s+k+n-m,-s|e^{H(\mathbf{t})}\beta_m^{*}\cdots\beta_1^{*}\beta_n\cdots\beta_1g|k\rangle $ are given by using Toda Darboux transformations. Firstly notice that 2--Toda hierarchy can be viewed
Externí odkaz:
http://arxiv.org/abs/2408.09457
Publikováno v:
SIGMA 20 (2024), 110, 21 pages
In this paper, modified Toda (mToda) equation is generalized to form an integrable hierarchy in the framework of Sato theory, which is therefore called mToda hierarchy. Inspired by the fact that Toda hierarchy is 2-component generalization of usual K
Externí odkaz:
http://arxiv.org/abs/2408.09450
Autor:
Hereman, Willy, Göktaş, Ünal
Publikováno v:
Mathematical and Computational Applications 29(5), 91, 35pp (2024)
Using a scaling symmetry, it is shown how to compute polynomial conservation laws, generalized symmetries, recursion operators, Lax pairs, and bilinear forms of polynomial nonlinear partial differential equations thereby establishing their complete i
Externí odkaz:
http://arxiv.org/abs/2408.07973
Solutions of a generalized constrained discrete KP (gcdKP) hierarchy with constraint on Lax operator $L^k=(L^k)_{\geq m}+\sum_{i=1}^lq_i\Delta^{-1}\Lambda^mr_i$, are invesitigated by Darboux transformations $T_D(f)=f^{[1]}\cdot\Delta\cdot f^{-1}$ and
Externí odkaz:
http://arxiv.org/abs/2408.00383
In this paper, we mainly investigate Lax structure and tau function for the large BKP hierarchy, which is also known as Toda hierarchy of B type, or Hirota--Ohta--coupled KP hierarchy, or Pfaff lattice. Firstly, the large BKP hierarchy can be derived
Externí odkaz:
http://arxiv.org/abs/2404.09815
We consider the Calogero--Moser derivative nonlinear Schr\"odinger equation (CM-DNLS), which is an $L^{2}$-critical nonlinear Schr\"odinger equation with explicit solitons, self-duality, and pseudo-conformal symmetry. More importantly, this equation
Externí odkaz:
http://arxiv.org/abs/2404.09603
Autor:
Matsuno, Yoshimasa
A nonlocal nonlinear Schr\"odinger equation with focusing nonlinearity is considered which has been derived as a continuum limit of the Calogero-Sutherland model in an integrable classical dynamical system. The equation is shown to stem from the comp
Externí odkaz:
http://arxiv.org/abs/2302.05108
Publikováno v:
Nonlinearity, 36 5007 (2023)
We study the problem of propagation of an input electromagnetic pulse through a long two-level laser amplifier under trivial initial conditions. In this paper, we consider an unstable model described by the Maxwell-Bloch equations without spectral br
Externí odkaz:
http://arxiv.org/abs/2210.01175