<p>We investigate traveling wave solutions for a system of coupled nonlinear Schrödinger equations arising from two-component Bose-Einstein condensates with spin-orbit and Raman couplings. The presence of spin-orbit coupling breaks the Galilean invariance, making the existence of traveling waves a nontrivial problem. By minimizing the action functional on the associated Nehari manifold and using the concentration-compactness principle, we establish the existence of non-radial traveling solitary waves in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\mathbb {R}^d$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>d</mi> </msup> </math></EquationSource> </InlineEquation> (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$d=1,2,3$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>d</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>). Furthermore, we prove that as the frequency <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\omega \rightarrow +\infty $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ω</mi> <mo stretchy="false">→</mo> <mo>+</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation>, the rescaled profiles of the boosted ground states or ground states converge strongly in the energy space <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$(H^1(\mathbb {R}^d,\mathbb {C}))^2$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mo stretchy="false">(</mo> <msup> <mi>H</mi> <mn>1</mn> </msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>d</mi> </msup> <mo>,</mo> <mi mathvariant="double-struck">C</mi> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">)</mo> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> to the ground states of a stationary system without spin-orbit and Raman couplings.</p>

Traveling Waves for Bose-Einstein Condensates System with Spin-Orbit and Raman Couplings

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发表日期：

2026年8月4日

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Jun-Qi Guo,
Dun Zhao

摘要

We investigate traveling wave solutions for a system of coupled nonlinear Schrödinger equations arising from two-component Bose-Einstein condensates with spin-orbit and Raman couplings. The presence of spin-orbit coupling breaks the Galilean invariance, making the existence of traveling waves a nontrivial problem. By minimizing the action functional on the associated Nehari manifold and using the concentration-compactness principle, we establish the existence of non-radial traveling solitary waves in $\mathbb {R}^d$ $R^{d}$ ( $d=1,2,3$ $d = 1, 2, 3$ ). Furthermore, we prove that as the frequency $\omega \rightarrow +\infty $ $ω \to + \infty$ , the rescaled profiles of the boosted ground states or ground states converge strongly in the energy space $(H^1(\mathbb {R}^d,\mathbb {C}))^2$ ${(H^{1} (R^{d}, C))}^{2}$ to the ground states of a stationary system without spin-orbit and Raman couplings.