arXiv subjects

Mohamed Bensaid

Publications and source records attributed to Mohamed Bensaid.

3 recordsLinked to original sources

arXiv2026

Existence of multi-solitons for logarithmic Schr{ö}dinger equation with a perturbation of a smooth $L^2$-subcritical function nonlinearity

In this paper, we study the nonlinear Schr{ö}dinger equation with a nonlinearity combining a focusing logarithmic term and a smooth $L^2$-subcritical function. Our main result is the construction of multisoliton solutions for this equation. These special configurations behave asymptotically, for large times, as the superposition of several solitons moving with distinct velocities. The proof relies on an iterative construction method combined with localized energy estimates adapted to the mixed structure of the nonlinearity.

math.AP↗

arXiv2026

The Cauchy problem for logarithmic Schr{ö}dinger equation with a perturbation of power law nonlinearity

In this paper, we study the Cauchy problem for the nonlinear Schr{ö}dinger equation with a nonlinearity combining a logarithmic term and a local nonlinearity which has polynomial growth. Our main result is the construction of solutions in the energy space $W_1(R^d)$ in the subcritical case. We also discuss a sufficient condition for global existence in the $L^2$-critical case in each of these spaces. Moreover, we establish a more general Cauchy theory in the space $Σ_α$, as introduced without details in [6].

math.AP↗

arXiv2025

Sato tau functions and construction of Somos sequence

In this short article, we will reconstruct the KP equation from Plucker relations and provide some generalizations on this topic. Additionally, in the final section, we define the discrete function $τ$ in a similar manner, leading to the construction of an integer sequence that has not yet been listed in the OEIS. Furthermore, this approach allows us to construct many other sequences that are not listed in the OEIS.

math.NT↗