science

List of integrable models

List of integrable models is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand List of integrable models rather than just read about it. In short: This is a list of integrable models as well as classes of integrable models in physics. Integrable models in 1+1 dimensions In classical and quantum field theory: free boson free fermion sine-Gordon model Thirring model sinh-Gordon model Liouville field theory Bullough–Dodd model Dym equation Calogero–Degasperis–Fokas equation Camassa–Holm equation Drinfeld–Sokolov–Wilson equation Benjamin–Ono equation SS model saus…

Key takeaways

List of integrable models belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect List of integrable models to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of List of integrable models from memory before moving on to harder problems.

Reference excerpt

This is a list of integrable models as well as classes of integrable models in physics.

Integrable models in 1+1 dimensions In classical and quantum field theory:

free boson free fermion sine-Gordon model Thirring model sinh-Gordon model Liouville field theory Bullough–Dodd model Dym equation Calogero–Degasperis–Fokas equation Camassa–Holm equation Drinfeld–Sokolov–Wilson equation Benjamin–Ono equation SS model sausage model Toda field theories O(N)-symmetric non-linear sigma models Ernst equation massless Schwinger model supersymmetric sine-Gordon model supersymmetric sinh-Gordon model conformal minimal models critical Ising model tricritical Ising model 3-state Potts model various perturbations of conformal minimal models superconformal minimal models Wess–Zumino–Witten model Nonlinear Schroedinger equation Korteweg–de Vries equation modified Korteweg–de Vries equation Gardner equation Gibbons–Tsarev equation Hunter–Saxton equation Kaup–Kupershmidt equation XXX spin chain XXZ spin chain XYZ spin chain 6-vertex model 8-vertex model Kondo Model Anderson impurity model Chiral Gross–Neveu model

Integrable models in 2+1 dimensions Ishimori equation Kadomtsev–Petviashvili equation Landau–Lifshitz–Gilbert equation Novikov–Veselov equation

Integrable models in 3+1 dimensions Self-dual Yang–Mills equations Systems with contact Lax pairs

In quantum mechanics harmonic oscillator hydrogen atom Hooke's atom (Hookium) Ruijsenaars–Schneider models Calogero–Moser models Inverse square root potential Lambert-W step-potential Multistate Landau–Zener Models

See also List of quantum-mechanical systems with analytical solutions List of some well-known classical integrable systems

References

Worked examples

Example 1 — a first encounter with List of integrable models

Start with the simplest possible case. Write down what List of integrable models claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to List of integrable models before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about List of integrable models ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of List of integrable models

In research: List of integrable models appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses List of integrable models in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: List of integrable models is common in secondary-school and first-year university syllabi. It links to neighbouring topics Exactly solvable models, Integrable systems, so understanding it makes those chapters shorter.
In everyday life: Look for List of integrable models outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study List of integrable models in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what List of integrable models means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain List of integrable models out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is List of integrable models in simple terms?

This is a list of integrable models as well as classes of integrable models in physics. Integrable models in 1+1 dimensions In classical and quantum field theory: free boson free fermion sine-Gordon model Thirring model sinh-Gordon model Liouville field theory Bullough–Dodd model Dym equation Calog…

Why does List of integrable models matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study List of integrable models?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on List of integrable models.