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4. Nonlinear Systems of Two Hyperbolic Equations

  1. utt = ax−n(xnux)x + uf(bu − cw) + g(bu − cw),   wtt = ax−n(xnwx)x + wf(bu − cw) + h(bu − cw).
  2. utt = ax−n(xnux)x + eλuf(λu − σw),   wtt = bx−n(xnwx)x + eσwg(λu − σw).
  3. utt = ax−n(xnux)x + uf(u/w),   wtt = bx−n(xnwx)x + wg(u/w).
  4. utt = ax−n(xnux)x + uf(u/w) + u/w h(u/w),   wtt = ax−n(xnwx)x + wg(u/w) + h(u/w).
  5. utt = ax−n(xnux)x + ukf(u/w),   wtt = bx−n(xnwx)x + wkg(u/w).
  6. utt = ax−n(xnux)x + uf(x, ukwm),   wtt = bx−n(xnwx)x + wg(x, ukwm).
  7. utt = ax−n(xnux)x + uf(u2 + w2) − wg(u2 + w2),   wtt = ax−n(xnwx)x + wf(u2 + w2) + ug(u2 + w2).
  8. utt = ax−n(xnux)x + uf(u2 − w2) + wg(u2 − w2),   wtt = ax−n(xnwx)x + wf(u2 − w2) + ug(u2 − w2).

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