<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>P</mml:mi> <mml:mi>T</mml:mi> </mml:mrow> </mml:math> -symmetric branched optical lattices: Spectral properties and stability of solitons

Authors: O K Tojakhmadova, T Akhmadjanov, M E Akramov

Publication: Chinese Physics B

Published: Sep 1, 2026

Source: Crossref

Back to Search View Original Cite This Article

Abstract

<jats:title>Abstract</jats:title> <jats:p> We propose a model for tunable <jats:inline-formula> <jats:tex-math> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="script">P</mml:mi> <mml:mi mathvariant="script">T</mml:mi> </mml:mrow> </mml:math> </jats:inline-formula> -symmetric branched optical lattices by investigating both linear and nonlinear Schrödinger equations with a <jats:inline-formula> <jats:tex-math> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="script">P</mml:mi> <mml:mi mathvariant="script">T</mml:mi> </mml:mrow> </mml:math> </jats:inline-formula> -symmetric periodic potential on the graph and solving them by imposing weighted vertex boundary conditions. A constraint derived from these vertex conditions determines the exceptional point of the system. In the <jats:inline-formula> <jats:tex-math> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="script">P</mml:mi> <mml:mi mathvariant="script">T</mml:mi> </mml:mrow> </mml:math> </jats:inline-formula> -unbroken phase, this constraint enforces <jats:inline-formula> <jats:tex-math> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="script">P</mml:mi> <mml:mi mathvariant="script">T</mml:mi> </mml:mrow> </mml:math> </jats:inline-formula> -symmetric boundary conditions at the vertices, ensuring a purely real spectrum; its violation leads to the emergence of complex eigenvalues in the linear regime. In the nonlinear regime, the same constraint determines the linear stability of solitons: satisfying the constraint yields stable solitons, whereas violating it corresponds to unstable solitons. </jats:p>

Keywords

constraint symmetric linear conditions solitons

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>P</mml:mi> <mml:mi>T</mml:mi> </mml:mrow> </mml:math> -symmetric branched optical lattices: Spectral properties and stability of solitons

Abstract

Keywords

Related Articles

Exploring Geographic Differences in High School Math Curricula, College Enrollment, and Postsecondary Math Remediation

Weeding Rake Design, Fabrication and Performance Evaluation

Children’s vocabulary predicts their math abilities: The mediating role of verbal and visuospatial short-term memory

Further constructions of permutation polynomials of the form &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;$ x+\gamma\operatorname{Tr}_{q}^{q^{2}}(h(x)) $&lt;/tex-math&gt;&lt;/inline-formula&gt; over finite fields with even characteristic

On the difference between perfect powers and integral S-units

Further constructions of permutation polynomials of the form <inline-formula><tex-math id="M1">$ x+\gamma\operatorname{Tr}_{q}^{q^{2}}(h(x)) $</tex-math></inline-formula> over finite fields with even characteristic