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Dergiler / Proceedings of International Mathematical Sciences / 2026 / Volume: 8 Issue: 1

A spectral fractional Hirota bilinear formulation]{A spectral fractional Hirota bilinear formulation for a time-fractional nonlinear Schr\"odinger flow: one-soliton solution and obstruction to finite two-soliton truncation

Subhasis Ray(Visva-Bharati)0000-0003-1100-4632
Sayfa
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Yayın Tarihi
2026-06-29
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Numerical residual plots illustrate the mismatch.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:We define a skew-adjoint spectral time-fractional operator $\mathcal{D}_t^\alpha$ ($0<\alpha\le1$) by the Fourier multiplier $\widehat{\mathcal{D}_t^\alpha\varphi}(\omega)=\mathrm{i}\,\mathrm{sgn}(\omega)|\omega|^\alpha\hat\varphi(\omega)$.
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Temel Bulgular & Veri:Using the induced fractional Hirota $D_t^\alpha$-operator we derive a bilinear system for a time-fractional focusing NLS flow, recovering the classical Hirota form when $\alpha=1$.
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Sonuç & Katkı:Numerical residual plots illustrate the mismatch.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:time-fractional nonlinear Schr\"odinger equation · Hirota bilinear method · spectral fractional derivative

Abstract

We define a skew-adjoint spectral time-fractional operator $\mathcal{D}_t^\alpha$ ($0<\alpha\le1$) by the Fourier multiplier $\widehat{\mathcal{D}_t^\alpha\varphi}(\omega)=\mathrm{i}\,\mathrm{sgn}(\omega)|\omega|^\alpha\hat\varphi(\omega)$. This provides a single-valued exponential Hirota calculus. Using the induced fractional Hirota $D_t^\alpha$-operator we derive a bilinear system for a time-fractional focusing NLS flow, recovering the classical Hirota form when $\alpha=1$. A stationary bright one-soliton $\tau$-function is obtained with dispersion relation $\omega=k^{2/\alpha}$. For $0<\alpha<1$ we prove that the classical finite two-soliton Hirota truncation is generically inconsistent: interaction-mode matching forces identities such as $(2\omega_2-\omega_1)^\alpha=2\omega_2^\alpha-\omega_1^\alpha$, contradicting strict concavity. Numerical residual plots illustrate the mismatch.

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Bu Makaleye Atıf Yap

Ray, S. (2026). A spectral fractional Hirota bilinear formulation]{A spectral fractional Hirota bilinear formulation for a time-fractional nonlinear Schr\"odinger flow: one-soliton solution and obstruction to finite two-soliton truncation. Proceedings of International Mathematical Sciences, Volume: 8 Issue: 1. https://doi.org/10.47086/pims.1866476

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Kaynakça (9)

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