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GROUP-INVARIANT SOLUTIONS, NON-GROUP-INVARIANT SOLUTIONS AND CONSERVATION LAWS OF QIAO EQUATION
Summary: This paper considers a completely integrable nonlinear wave equation which is called Qiao equation. The equation is reduced via Lie symmetry analysis. Two classes of new exact group-invariant solutions are obtained by solving the reduced equations.
Shi, Jianping, Zhou, Mengmeng, Fang, Hui
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Solutions of Abreu's Equation with Rotation Invariance [PDF]
In the paper under review some fourth order nonlinear partial differential equation in an \(n\)-dimensional Cartesian space \({\mathbb R}^{n}\) named Abreu's equation [see \textit{S. K. Donaldson}, J. Differ. Geom., 62, No. 2, 289--349 (2002; Zbl 1074.53059)], in the context of Kähler metrics on tori varietes, are considered.
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ABSTRACT Background Latino children are projected to make up nearly one‐third of United States (US) children by 2060, and many of their caregivers speak Spanish. Prior survey research has documented communication difficulties for Spanish‐speaking caregivers of children with cancer, but contemporary qualitative data are limited.
Jenny Ruiz +6 more
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On invariance of schemes in the method of fundamental solutions
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Koya Sakakibara, Shigetoshi Yazaki
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Optimal Algebra and Invariant Solutions for Chazy’s Equation [PDF]
We characterized the invariant solutions for Chazy’s equation using the generators of the optimal algebra, which was obtained using Lie group symmetries for the ...
Loaiza, G +2 more
core
ABSTRACT Background Young adult childhood cancer survivors (YA‐CCS) have an increased risk of treatment‐related health complications throughout their lives. Lifelong survivorship care is recommended, yet many YA‐CCS experience disruptions in care during pediatric‐to‐adult transitions and do not receive recommended survivorship care.
Kevin Shanchen Pu +8 more
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ABSTRACT Background Chronic micro‐inflammation in patients with end‐stage renal disease (ESRD) is a significant driver of cardiovascular complications and diminished quality of life. While standard hemodialysis (SHD) effectively manages small‐molecule clearance, its ability to remove medium‐to‐large uremic toxins—the primary catalysts of systemic ...
Hongwei Zuo +5 more
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Optimal System, Reductions, and Conservation Laws of a Nonlinear Damped Klein-Gordon- Fock Equation
A detailed Lie symmetry analysis of the nonlinear damped Klein-Gordon Fock equation: $u_{tt}\,+\alpha (u)\,u_{t}\,=\,u_{xx}\,+\,f(u)$ is addressed in this paper.
Faiza Arif +3 more
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Lift of Invariant to Non-Invariant Solutions of Complex Monge-Ampère Equations [PDF]
We show how partner symmetries of the elliptic and hyperbolic complex Monge-Ampère equations (CMA and HCMA) provide a lift of non-invariant solutions of three- and two-dimensional reduced equations, i.e., a lift of invariant solutions of the original CMA and HCMA equations, to non-invariant solutions of the latter four-dimensional equations.
Sheftel, M. B., Malykh, A. A.
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Survey of Eight Modern Methods of Hamiltonian Mechanics
Here we describe eight new methods, arisen in the last 60 years, to study solutions of a Hamiltonian system with n degrees of freedom. The first six of them are intended for systems with small parameters or without them.
Alexander D. Bruno, Alexander B. Batkhin
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