The usage of tag-removed was two-fold: as an 'empty' tag for massively off-topic and mistagged questions. as a tool to 'delete' tags via merging them into it. Due to the second use-case numerous legitimate questions also got this tag. I think it could make sense to go over this list and reta...
I have this system of $n$ non-linear equations in $n$ unknowns, arising out of my research problem. Given that $x_0=1$, I have to solve for $(x_1,x_2,\ldots,x_n).$ $$\sum_{i=0}^n x_i^2+2\sum_{j=1}^n\sum_{i=0}^{n-j}x_ix_{i+j}=1$$ $$\sum_{j=1}^n\sum_{i=0}^{n-j}~j^2~x_ix_{i+j}=0$$ $$\sum_{j=1}^n\sum...
I am looking for an exact solution for the following special case of Chini Equation with $2\geq a > 1 > b > 0, x, y \in \mathbb{R}^+$, $$\frac{dy}{dx} = 1 + \frac{a}{y} + \frac{b}{x}$$ I have tried to approach this using multiple methods and substitutions, but none has gotten me far. I know tha...
Would anybody be able to share a Mathematica/Matlab/other script for calculating Onsager's exact solution for the magnetisation of the 2d Ising model? I would be most grateful of one in order to test my MC simulations of the system.
I am looking for an exact solution to equation: $w''=aw^{-1/3}+b[f(y)]w^{-5/3}$, where $w=w(y), f(y)$ - arbitrary function (in this case $y^n$ with arbitrary $n$); $a,b$ - constants. Of course I can solve it using numerical methods for certain initial conditions, but I was looking for a exact s...
The nonlinear pde $$ \partial_t^2\phi-\partial_x^2\phi+\lambda\phi^3=0 $$ has the exact solution $$ \phi(x,t)=\mu\left(\frac{2}{\lambda}\right)^\frac{1}{4}{\rm sn}(p_0t-p\cdot x+\varphi,i) $$ with $\mu$ and $\varphi$ two integration constants and sn the snoidal Jacobi function, provided the...
It is common to solve PDEs with e.g. Fourier and Laplace Transforms. It is often said that Wavelets are a progression compared to them with many nice features. My question: Which Ansätze do you know to solve PDEs with Wavelets? Are these solution methods actually superior to the classical Ansätz...
I have this system of $n$ non-linear equations in $n$ unknowns, arising out of my research problem. Given that $x_0=1$, I have to solve for $(x_1,x_2,\ldots,x_n).$ $$\sum_{i=0}^n x_i^2+2\sum_{j=1}^n\sum_{i=0}^{n-j}x_ix_{i+j}=1$$ $$\sum_{j=1}^n\sum_{i=0}^{n-j}~j^2~x_ix_{i+j}=0$$ $$\sum_{j=1}^n\sum...
I am looking for an exact solution for the following special case of Chini Equation with $2\geq a > 1 > b > 0, x, y \in \mathbb{R}^+$, $$\frac{dy}{dx} = 1 + \frac{a}{y} + \frac{b}{x}$$ I have tried to approach this using multiple methods and substitutions, but none has gotten me far. I know tha...
I am looking for an exact solution to equation: $w''=aw^{-1/3}+b[f(y)]w^{-5/3}$, where $w=w(y), f(y)$ - arbitrary function (in this case $y^n$ with arbitrary $n$); $a,b$ - constants. Of course I can solve it using numerical methods for certain initial conditions, but I was looking for a exact s...
The nonlinear pde $$ \partial_t^2\phi-\partial_x^2\phi+\lambda\phi^3=0 $$ has the exact solution $$ \phi(x,t)=\mu\left(\frac{2}{\lambda}\right)^\frac{1}{4}{\rm sn}(p_0t-p\cdot x+\varphi,i) $$ with $\mu$ and $\varphi$ two integration constants and sn the snoidal Jacobi function, provided the...
It is common to solve PDEs with e.g. Fourier and Laplace Transforms. It is often said that Wavelets are a progression compared to them with many nice features. My question: Which Ansätze do you know to solve PDEs with Wavelets? Are these solution methods actually superior to the classical Ansätz...
In the theory of indefinite sums, anti-differences and finite calculus, the following difference functional equation and its solutions are very important: $$\bigtriangleup F(x):=F(x+1)-F(x)=f(x) \quad\quad(1),$$ where $\bigtriangleup$ is the forward difference operato...
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