diff --git a/src/scgenerator/evaluator.py b/src/scgenerator/evaluator.py
index 3ed4a03..a34449e 100644
--- a/src/scgenerator/evaluator.py
+++ b/src/scgenerator/evaluator.py
@@ -5,6 +5,8 @@ from typing import Any, Callable, Optional, Union
 
 import numpy as np
 
+from scgenerator import solver
+
 from . import math, operators, utils
 from .const import MANDATORY_PARAMETERS
 from .errors import EvaluatorError, NoDefaultError
@@ -377,7 +379,17 @@ default_rules: list[Rule] = [
     Rule("raman_op", operators.NoRaman, priorities=-1),
     Rule("loss_op", operators.NoLoss, priorities=-1),
     Rule("plasma_op", operators.NoPlasma, priorities=-1),
-    Rule("conserved_quantity", operators.NoConservedQuantity, priorities=-1),
+    # solvers
+    Rule("integrator", solver.ConstantStepIntegrator, conditions=dict(adapt_step_size=False)),
+    Rule(
+        "integrator",
+        solver.ConservedQuantityIntegrator,
+        conditions=dict(adapt_step_size=True),
+        priorities=1,
+    ),
+    Rule("integrator", solver.RK4IPSD, conditions=dict(adapt_step_size=True)),
+    Rule("integrator", solver.ERK43, conditions=dict(adapt_step_size=True)),
+    Rule("integrator", solver.ERK54, conditions=dict(adapt_step_size=True), priorities=1),
 ]
 
 envelope_rules = default_rules + [
diff --git a/src/scgenerator/solver.py b/src/scgenerator/solver.py
index 9ca8987..83408ab 100644
--- a/src/scgenerator/solver.py
+++ b/src/scgenerator/solver.py
@@ -72,6 +72,16 @@ class Integrator(ValueTracker):
     def nl(self, spectrum: np.ndarray) -> np.ndarray:
         return self.nonlinear_operator(self.state.replace(spectrum))
 
+    def accept_step(
+        self, new_state: CurrentState, previous_step_size: float, next_step_size: float
+    ) -> CurrentState:
+        self.state = new_state
+        self.state.current_step_size = next_step_size
+        self.state.z += previous_step_size
+        self.state.step += 1
+        self.logger.debug(f"accepted step {self.state.step} with h={previous_step_size}")
+        return self.state
+
 
 class ConstantStepIntegrator(Integrator):
     def __init__(
@@ -87,7 +97,7 @@ class ConstantStepIntegrator(Integrator):
             lin = self.linear_operator(self.state)
             nonlin = self.nonlinear_operator(self.state)
             self.record_tracked_values()
-            new_spec = rk4ip_step(
+            self.state.spectrum = rk4ip_step(
                 self.nonlinear_operator,
                 self.state,
                 self.state.spectrum,
@@ -95,11 +105,11 @@ class ConstantStepIntegrator(Integrator):
                 lin,
                 nonlin,
             )
-
-            self.state.z += self.state.current_step_size
-            self.state.step += 1
-            self.state = new_spec
-            yield self.state
+            yield self.accept_step(
+                self.state,
+                self.state.current_step_size,
+                self.state.current_step_size,
+            )
 
 
 class ConservedQuantityIntegrator(Integrator):
@@ -156,11 +166,7 @@ class ConservedQuantityIntegrator(Integrator):
                     f"step {new_state.step} rejected : {h=}, {self.current_error=}, {h_next_step=}"
                 )
             self.last_qty = new_qty
-            self.state = new_state
-            self.state.current_step_size = h_next_step
-            self.state.z += h
-            self.state.step += 1
-            yield self.state
+            yield self.accept_step(new_state, h, h_next_step)
 
     def values(self) -> dict[str, float]:
         return dict(cons_qty=self.last_qty, relative_error=self.current_error)
@@ -204,11 +210,8 @@ class RK4IPSD(Integrator):
                     h_next_step = h * size_fac
                     break
 
-            self.state.current_step_size = h_next_step
-            self.state.z += h
-            self.state.step += 1
-            self.state = new_fine
-            yield self.state
+            self.state.spectrum = new_fine
+            yield self.accept_step(self.state, h, h_next_step)
 
     def take_step(
         self, h: float, spec: np.ndarray, lin: np.ndarray, nonlin: np.ndarray
@@ -284,12 +287,9 @@ class ERK43(Integrator):
                     f"step {self.state.step} rejected : {h=}, {self.current_error=}, {h_next_step=}"
                 )
 
-            self.state.current_step_size = h_next_step
-            self.state.z += h
-            self.state.step += 1
-            self.state = new_fine
             k5 = tmp_k5
-            yield self.state
+            self.state.spectrum = new_fine
+            yield self.accept_step(self.state, h, h_next_step)
 
     def values(self) -> dict[str, float]:
         return dict(
@@ -341,12 +341,9 @@ class ERK54(ERK43):
                 self.logger.info(
                     f"step {self.state.step} rejected : {h=}, {self.current_error=}, {h_next_step=}"
                 )
-            self.state.current_step_size = h_next_step
-            self.state.z += h
-            self.state.step += 1
-            self.state = new_fine
             k7 = tmp_k7
-            yield self.state
+            self.state.spectrum = new_fine
+            yield self.accept_step(self.state, h, h_next_step)
 
 
 def rk4ip_step(