Analysis and Mathematical Physics

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Global existence and blow-up for wave equation of p-Laplacian type
Analysis and Mathematical Physics - - 2023
Ge Zu, Lili Sun, Jiacheng Wu
This article explores a quasilinear wave equation of p-Laplacian type: $$\begin{aligned} u_{tt}-\Delta _{p}u-\Delta u_t=|u|^{r-1}u \end{aligned}$$ in a bounded domain $$\Omega \subset \mathbb {R}^{3}$$ ...... hiện toàn bộ
Lump and lump-soliton solutions to the $$(2+1)$$ -dimensional Ito equation
Analysis and Mathematical Physics - Tập 8 - Trang 427-436 - 2017
Jin-Yun Yang, Wen-Xiu Ma, Zhenyun Qin
Based on the Hirota bilinear form of the $$(2+1)$$ -dimensional Ito equation, one class of lump solutions and two classes of interaction solutions between lumps and line solitons are generated through analysis and symbolic computations with Maple....... hiện toàn bộ
On spectral asymptotic of quasi-exactly solvable quartic potential
Analysis and Mathematical Physics - - 2021
Boris Shapiro, Miloš Tater
Motivated by the earlier results of Masoero and De Benedetti (Nonlinearity 23:2501, 2010) and Shapiro et al. (Commun Math Phys 311(2):277–300, 2012), we discuss below the asymptotic of the solvable part of the spectrum for the quasi-exactly solvable quartic oscillator. In particular, we formulate a conjecture on the coincidence of the asymptotic shape of the level crossings of the latter oscillato...... hiện toàn bộ
Solving the inverse Sturm–Liouville problem with singular potential and with polynomials in the boundary conditions
Analysis and Mathematical Physics - Tập 13 - Trang 1-35 - 2023
Egor E. Chitorkin, Natalia P. Bondarenko
In this paper, we for the first time get constructive solution for the inverse Sturm–Liouville problem with complex-valued singular potential and with polynomials of the spectral parameter in the boundary conditions. The uniqueness of recovering the potential and the polynomials from the Weyl function is proved. An algorithm of solving the inverse problem is obtained and justified. More concretely...... hiện toàn bộ
Laguerre polynomials and transitional asymptotics of the modified Korteweg–de Vries equation for step-like initial data
Analysis and Mathematical Physics - Tập 9 - Trang 1761-1818 - 2018
M. Bertola, A. Minakov
We consider the compressive wave for the modified Korteweg–de Vries equation with background constants $$c>0$$ for $$x\rightarrow -\infty $$ and 0 for $$x\rightarrow +\infty $$. We study the asymptotics of solutions in the transition zone $$4c^2t-\varepsilon t0,$$$$\sigma \in (0,1),$$$$\beta >0.$$ In this region we have a bulk of nonvanishing os...... hiện toàn bộ
Necessary and sufficient conditions for the bounds of the commutator of a Littlewood-Paley operator with fractional differentiation
Analysis and Mathematical Physics - Tập 9 - Trang 2109-2132 - 2019
Xiongtao Wu, Yanping Chen, Liwei Wang, Wenyu Tao
For $$b\in L_{\mathrm{loc}}({\mathbb {R}}^n)$$ and $$0<\alpha <1$$, we use fractional differentiation to define a new type of commutator of the Littlewood-Paley g-function operator, namely $$\begin{aligned} g_{\Omega ,\alpha ;b}(f )(x) =\bigg (\int _0^\infty \bigg |\frac{1}{t} \int _{|x-y|\le t}\frac{\Omega (x-y)}{|x-y|^{n+\alpha -1}}(b(x)-b(y))f(y)\,dy\bigg |^2\frac{dt}{t}\bigg )^{1/2}. \end{alig...... hiện toàn bộ
A series expansion for generalized harmonic functions
Analysis and Mathematical Physics - Tập 11 - Trang 1-28 - 2021
Markus Klintborg, Anders Olofsson
We consider a class of generalized harmonic functions in the open unit disc in the complex plane. Our main results concern a canonical series expansion for such functions. Of particular interest is a certain individual generalized harmonic function which suitably normalized plays the role of an associated Poisson kernel.
Nonlinear splittings on fibre bundles
Analysis and Mathematical Physics - Tập 12 - Trang 1-28 - 2021
S. Hajdú, T. Mestdag
We introduce the notion of a nonlinear splitting on a fibre bundle as a generalization of an Ehresmann connection. We present its basic properties and we pay attention to the special cases of affine, homogeneous and principal nonlinear splittings. We explain where nonlinear splittings appear in the context of Lagrangian systems and Finsler geometry and we show their relation to Routh symmetry redu...... hiện toàn bộ
N-fold Darboux transformations and exact solutions of the combined Toda lattice and relativistic Toda lattice equation
Analysis and Mathematical Physics - Tập 10 Số 3 - Trang 1-21 - 2020
Fan, Fang-Cheng, Xu, Zhi-Guo, Shi, Shao-Yun
In this paper, the N-fold Darboux transformation (DT) of the combined Toda lattice and relativistic Toda lattice equation is constructed in terms of determinants. Comparing with the usual 1-fold DT of equations, this kind of N-fold DT enables us to generate the multi-soliton solutions without complicated recursive process. As applications of the N-fold DT, we derive two kinds of N-fold explicit ex...... hiện toàn bộ
Epsilon coherent states with polyanalytic coefficients for the harmonic oscillator
Analysis and Mathematical Physics - Tập 9 - Trang 367-383 - 2017
Zouhaïr Mouayn
We construct a new class of coherent states indexed by points z of the complex plane and depending on two positive parameters m and $$ \varepsilon >0$$ by replacing the coefficients ...... hiện toàn bộ
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