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<p>The paper is concerned with the generalized Kadomtsev–Petviashvili equations in dimensions 2 and 3 with homogeneous nonlinearity of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>-supercritical power. By solving a minimization problem with two constraints we prove the existence of a ground state solution (a least energy solution under the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> constraint) for all possible prescribed norms.</p>

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Normalized solutions to the generalized Kadomtsev–Petviashvili equations: supercritical case

  • 期刊论文

  • 发表日期：

    2026年2月2日

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  • Jianqing Chen,
  • Xiaopeng Huang,
  • Zhi-Qiang Wang

摘要

The paper is concerned with the generalized Kadomtsev–Petviashvili equations in dimensions 2 and 3 with homogeneous nonlinearity of \(L^2\) L 2 -supercritical power. By solving a minimization problem with two constraints we prove the existence of a ground state solution (a least energy solution under the \(L^2\) L 2 constraint) for all possible prescribed norms.