Results 61 to 70 of about 1,069 (170)
On Bäcklund Transformations for Nonlinear Partial Differential Equations [PDF]
, 1995 In this paper, Bäcklund transformations for nonlinear partial differential equations are obtained without using any structure associated with the equations. We classify all the nonlinear partial differential equations of the form uxxx = F(u, ux, ut) that
Wu, H.Y.
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Ain Shams Engineering JournalThis research investigates the extended Kadomtsev-Petviashvili-Boussinesq equation, relevant in numerous scenarios involving dissipative media. To initiate the analysis, a Hirota bilinear form is applied, leading to a Bäcklund transformation for the ...
Nauman Raza +4 more
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Journal of Neurochemistry, Volume 170, Issue 7, July 2026.Parkinson's disease (PD) is characterized by the progressive loss of dopaminergic neurons in the midbrain. Cell transplantation, which aims to replace these lost neurons, has emerged as a promising approach. Early attempts using fetal ventral mesencephalic tissue showed proof‐of‐concept, with some patients achieving long‐term motor improvement. However,
Etsuro Nakanishi +4 more
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Engineering Reports, Volume 8, Issue 6, June 2026.This study investigates a nonlinear Navier‐Stokes‐type model for elastic cylindrical vessels. Exact solutions are derived via the Bäcklund transformation and the ϕ6$$ {\phi}^6 $$‐expansion method, and dynamical behaviors are analyzed using bifurcation and chaos tools, revealing diverse wave structures and parameter‐dependent propagation characteristics.
Sheikh Zain Majid +2 more
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Bilinear Bäcklund transformation, Lax pair and multi-soliton solution for a vector Ramani equation [PDF]
, 2017 In this paper, a vector Ramani equation is proposed by using the bilinear approach. With the help of the bilinear exchange formulae, bilinear Bäcklund transformation and the corresponding Lax pair for the vector Ramani equation are derived.
Junchao Chen, Bao-Feng Feng, Yong Chen
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Solitons, Cnoidal Waves and Nonlinear Effects in Oceanic Shallow Water Waves
Fractal and FractionalGravity water waves in the shallow-ocean scenario described by generalized Boussinesq–Broer–Kaup–Whitham (gBBKW) equations are discussed. The residual symmetry and Bäcklund transformation associated with the gBBKW equations are systematically constructed.
Huanhe Dong +3 more
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The Modified Camassa–Holm Equation on the Half Line: A Riemann–Hilbert Approach
Studies in Applied Mathematics, Volume 156, Issue 6, June 2026.ABSTRACT We consider the initial‐boundary value (IBV) problem for the modified Camassa–Holm (mCH) equation m∼t+(u∼2−u∼x2+2u∼)m∼x=0,m∼:=u∼−u∼xx+1$\tilde{m}_t+{\left((\tilde{u}^2-\tilde{u}_x^2+2\tilde{u})\tilde{m}\right)}_x = 0, \qquad \tilde{m}:=\tilde{u}-\tilde{u}_{xx}+1$ on the half‐line x≥0$x \ge 0$.
Iryna Karpenko, Dmitry Shepelsky
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BACKLUND TRANSFORMATIONS FOR LIOUVILLE’S EQUATIONS WITH EXPONENTIAL NONLINEARITY
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2020 Background. The study of Backlund 's transformations is one of the current topics in the theory of differential equations in partial derivatives. Such transformations are used to find solutions to nonlinear differential equations, including solitonic ...
T. V. Red'kina, O. V. Novikova
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Generation of a recipient line for Rubisco engineering by multiplex genome editing in tobacco
The Plant Journal, Volume 126, Issue 4, May 2026.SUMMARY Rubisco (ribulose 1,5‐bisphosphate carboxylase/oxygenase) is the primary CO2‐fixing enzyme on our planet. Its slow kinetics and poor discrimination between carbon dioxide and oxygen as substrates severely limit the efficiency of photosynthetic carbon fixation by plants.
Gonçalo E. da Silva +6 more
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On Darboux-Bäcklund Transformation and Positon Type Solution of Coupled Nonlinear Optical Waves [PDF]
, 2000 A Darboux-Bäcklund transformation is used to obtain a positon type solution of the nonlinear equations describing the propagation of coupled nonlinear optical pulses.This form of the positon solution is then compared with that obtained by the special ...
Sen, D. C., Chowdhury, A. R.
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